geometry step by step problem solving

Math Solver

Geogebra math solver.

Get accurate solutions and step-by-step explanations for algebra and other math problems, while enhancing your problem-solving skills!

• Privacy Policy

eMathHelp Math Solver - Free Step-by-Step Calculator

Solve math problems step by step.

At eMathHelp, we provide a wealth of mathematical calculators designed to simplify your daily computations, whether you need to tackle complex equations or perform fundamental math operations.

Our Calculator Categories

Algebra calculator.

Explore our Algebra Calculator, designed to help solve equations, factor polynomials, and more, making algebra more accessible to you.

Geometry Calculator

Our Geometry Calculator is your handy tool for working with triangles.

Pre-Calculus Calculator

Solve pre-calculus problems with our specialized calculator, helping you master foundational math concepts before diving into advanced mathematics.

Calculus Calculator

Improve your calculus knowledge with our Calculus Calculator, which makes complex operations like derivatives, integrals, and differential equations easy.

Linear Algebra Calculator

Perform matrix operations and solve systems of linear equations with our Linear Algebra Calculator, essential for fields like physics and engineering.

Discrete Math Calculator

Tackle discrete mathematical problems confidently with our specialized calculator, ideal for computer science, cryptography, and more.

Probability and Statistics Calculator

Make data analysis a breeze with our Probability and Statistics Calculator, which helps you extract meaningful insights from your data.

Linear Programming Calculator

Optimize linear objective functions easily using our Linear Programming Calculator, which is valuable in resource allocation and economics.

Who Are We?

eMathHelp is a team of dedicated math enthusiasts who believe everyone should have access to powerful mathematical tools. Our mission is to make math more approachable and enjoyable for people of all ages and backgrounds.

Why Choose Our Calculators?

Versatility.

We offer a wide range of calculators for math, including algebraic and calculus tools, making it your one-stop destination for all your mathematical needs.

Our user-friendly interface ensures that even complex calculations can be performed effortlessly, making math accessible to everyone.

Our calculator is designed to provide precise results, helping you save time and eliminate errors.

Diverse Categories of Calculators

We cover various mathematical concepts and topics, from simple to complex.

Our Most Popular Math Calculators

Definite and improper integral calculator.

Solve complex integration problems, including improper integrals, quickly.

Efficiently optimize resources by solving linear programming problems.

Integral Calculator

Easily find antiderivatives by applying different techniques.

Function Calculator

Find the main properties of functions easily.

Discriminant Calculator

Quickly analyze quadratic equations.

What types of calculations can the online math calculator perform?

Our online math calculator offers a wide range of operations to perform. You can use it to solve equations, find derivatives, factor expressions, and more.

Are the online math calculators free to use?

Absolutely! We provide free calculators for math, ensuring you can access powerful mathematical tools without cost. No subscriptions or hidden fees.

How many online math calculators do you offer?

We offer a wide range of online math calculators covering a variety of math topics.

Do the calculators provide step-by-step solutions?

Many of our calculators provide detailed, step-by-step solutions. This will help you better understand the concepts that interest you.

Get step-by-step solutions to your math problems

Try Math Solver

Get step-by-step explanations

Graph your math problems

Practice, practice, practice

Get math help in your language

• Homework Help
• Article Directory

How to Do Geometry Problems: Step-By-Step Solutions

•  / 

You'll encounter lots of different types of geometry problems in school, but many of them can be solved using the same basic approach. Read on for a step-by-step explanation of how to solve geometry problems.

Geometry Solutions

One of the most common types of geometry problems you'll be asked to solve is the kind in which you calculate a property of a shape. You'll be given some facts about a 2-dimensional object, like a rectangle or a circle, or a 3-dimensional object, like a cylinder or a cone. Then, you'll use that information to find a property of the shape, like perimeter or volume. To do this successfully, follow the steps below.

First, you'll need to assemble all of the facts that the problem gives you, like the length, height or diameter of the shape. In many cases, it helps if you draw a picture of the shape and label it with the information you're given.

The next step is to identify what the problem is asking you to do. Do you need to figure out the shape's volume, perimeter, area or surface area?

The third step is to identify the appropriate formula to calculate the value that's being asked for. Here are a few common formulas you may use:

Perimeter of a rectangle: 2(length) + 2(width)

Circumference of a circle: 2(3.14)(radius)

Area of a rectangle: length x width

Area of a circle: (3.14)(radius)^2

Area of a triangle: 1/2 x base x height

Volume of a rectangular prism: length x width x height

Plug your information into the formula and solve it. Don't forget to check your work!

Once you've solved your problem, there's one more step you need to complete before you're finished. One of the most common mistakes that students make when they're solving geometry problems is reporting their answers in the wrong type of unit. This can happen if you fail to notice that different parts of a problem are given in different units. For instance, the height of a rectangle might be given in meters, and its width might be given in centimeters. If you don't convert these measures into a single type of unit, you'll get the wrong answer.

It's also common for students to forget to report square or cubed units. If you're reporting area or surface area, your answer should be in square units, and if you're reporting volume, it should be in cubed units.

Other Articles You May Be Interested In

One plus one will always equal two...but just how students are taught math is going to change. Nearly every state in the country has adopted the Common Core Standards; for math, this means new and more in-depth approaches to teaching the subject. Have we seen the last of traditional algebra and geometry classes?

One of the most useful and widely used rules in mathematics is the Pythagorean theorem. Your child's mastery of this theorem is critical to success in geometry. One helpful method for understanding and remembering a rule like the Pythagorean theorem is to fully explore its meaning and history.

We Found 7 Tutors You Might Be Interested In

Huntington learning.

• What Huntington Learning offers:
• Online and in-center tutoring
• One on one tutoring
• Every Huntington tutor is certified and trained extensively on the most effective teaching methods
• What K12 offers:
• Online tutoring
• Has a strong and effective partnership with public and private schools
• AdvancED-accredited corporation meeting the highest standards of educational management

Kaplan Kids

• What Kaplan Kids offers:
• Customized learning plans
• Real-Time Progress Reports track your child's progress
• What Kumon offers:
• In-center tutoring
• Individualized programs for your child
• Helps your child develop the skills and study habits needed to improve their academic performance

Sylvan Learning

• What Sylvan Learning offers:
• Sylvan tutors are certified teachers who provide personalized instruction
• Regular assessment and progress reports

Tutor Doctor

• What Tutor Doctor offers:
• In-Home tutoring
• One on one attention by the tutor
• Develops personlized programs by working with your child's existing homework
• What TutorVista offers:
• Student works one-on-one with a professional tutor
• Using the virtual whiteboard workspace to share problems, solutions and explanations

Find the Perfect Tutor

Our commitment to you, free help from teachers, free learning materials, helping disadvantaged youth, learning tools.

• Make learning fun with these online games!
• Looking for ways to bring learning home? Check out our blog.

Want to Help Your Child Learn?

More articles.

• Homework Help for High School Math
• Common Behavioral Problems in Children
• Creating Your Own Math Problems and Worksheets
• Common Problems in Reading Faced by Older Students with Learning Disabilities
• How Practice Problems and Worksheets Can Alleviate Math Anxiety
• Do You Think the Drop Out Age Should Be Raised?
• Doing More with Less: Rural Schools and Student Health
• Keeping Schools Safe, But At What Cost?
• How to Improve Your Child's Attitude Toward Learning
• Math Homework: What to Expect and Why IT Is Important
• Advice for Military Homeschool Families
• Math Help Can Be Found Through Online Tutoring
• How Confidence Can Affect Children's Performances in School
• Recognizing Student Struggles 6 of 7: Identifying the Warning Sign--Class Standing
• A Guide to Off-Campus Housing
• College Study Tips
• Diabetic Teacher Fights to Have Life-Saving Pooch in the Classroom
• Celebrate World Teachers' Day!
• Books Before Bedtime The Napping House
• New York Public School Students Get Physical
• How Can a Parent Help a Slow Learner
• 9th Grade Reading List
• Addition Activities for Kids
• New York State 8th Grade Test
• Decimal Problems
• Elementary Geometry Problems
• Geometry Word Problems
• Elementary Geometry
• Geometry Tutorial
• Geometry for Kids
• Free Geometry Worksheets Grades 5 6
• Elementary Geometry Rhombus
• Elementary Geometry Worksheets
• Geometry Assistance
• Free Online Geometry Help
• Privacy Policy
• Resource Directory

© 2003 - 2024 All other trademarks and copyrights are the property of their respective owners. All rights reserved.

Step-by-Step Solutions

Use step-by-step calculators for chemistry, calculus, algebra, trigonometry, equation solving, basic math and more.

Gain more understanding of your homework with steps and hints guiding you from problems to answers! Wolfram|Alpha Pro step-by-step solutions not only give you the answers you're looking for, but also help you learn how to solve problems.

Starting at $ 5 .00 /month

Step-by-Step Solutions Features

Not just answers—step-by-step solutions buttons expand answers and explain how that answer was found.

Show Intermediate Steps

Break steps down even further with intermediate steps. These optional additional explanations for individual pieces of step-by-step solutions help guide you.

Choose a Method

Explore different ways of finding a solution. Use your classroom's teaching method to guide you through the answer.

Your own tutor—hints are also frequently provided to not just provide answers, but also to guide you towards finding the solution yourself.

Examples of Step-by-Step Solutions

Explore some of the content areas covered by step-by-step solutions, including math, chemistry and physics, or view more examples »

Equation Solving

More Math Topics

• Solve equations and inequalities
• Simplify expressions
• Factor polynomials
• Graph equations and inequalities
• Advanced solvers
• All solvers
• Arithmetics
• Determinant
• Percentages
• Scientific Notation
• Inequalities

What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

• The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
• The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
• The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
• The calculus section will carry out differentiation as well as definite and indefinite integration.
• The matrices section contains commands for the arithmetic manipulation of matrices.
• The graphs section contains commands for plotting equations and inequalities.
• The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

Math Topics

More solvers.

• Add Fractions
• Simplify Fractions

Please ensure that your password is at least 8 characters and contains each of the following:

• a special character: @$#!%*?&

o Identify some critical steps of the process for solving practical geometry problems

o Apply geometry problem-solving techniques to practical situations

Geometry has a variety of real-life applications in everyday situations. In this article, we will learn to apply geometric principles and techniques to solve problems. The key to solving practical geometry problems is translation of the real-life situation into figures, measurements, and other information necessary to represent the situation conceptually. For instance, you already know how to calculate the area of a composite figure; if you were asked to determine how much floor space is available in a certain building with a composite shape, you would simply need to apply the same principles as you would use for calculating the area of a composite figure. Some measurements of the building might, of course, be required, but the same problem-solving techniques apply.

It behooves us to present a basic approach to solving practical geometry problems. This approach is similar to that for solving almost a word problem, but is geared slightly more toward the characteristics of geometry problems in particular.

1. Determine what you need to calculate to solve the problem. In some cases, you may need a length; in others, an area or angle measure. If you are conscious throughout the process of what you need to determine, you can save yourself a significant amount of time.

2. Draw a diagram. Sometimes a straightedge, compass, protractor, or some combination of these tools can be helpful. Even if you only use a rough sketch, however, making a visual representation of the problem can help you organize your thoughts and keep track of important information such as the relationship of line segments and angles as well as the measures thereof.

3. Record all appropriate measurements. If you are calculating an area, for instance, you may need to take measurements of certain lengths (alternatively, these may be provided to you). In either case, record them and mark them in some manner on your diagram.

4. Pay attention to units. Using units of square meters for a length or angle measure can be an embarrassing mistake! Keep careful track of the units you are using throughout the problem. If no units are given, simply use the generic term "units" in place of inches or meters, for example.

5. Divide the figure, if necessary, into manageable portions. If your diagram is a composite figure, it may help to divide the figure into bite-sized portions that you can handle.

6. Identify any appropriate geometric relationships. This step can greatly simplify the problem. Perhaps you can show two triangles to be congruent or similar, or perhaps you can identify congruent segments or angles. Use this step to fill in as much missing information in your diagram as you can.

7. Do the math. At this point, you need to apply what you've learned to analyze the figure and other data to solve the problem. You may, for example, need to apply the Pythagorean theorem, or you may need to calculate the perimeter of a figure. Whatever the details of the problem, you will need to apply your skills in geometry in an appropriate manner.

8. Check your results. Take a look at your answer in the context of your diagram-does your answer make sense? A result of millions of square meters for the area of a figure with dimensions in the range of a few meters should tell you that you've made an error at some point in your analysis.

Not every step of the approach outlined above will be needed in every problem. You must use your best judgment in determining what is necessary to solve the problem in a satisfactory and time-efficient manner. Also, you may not always think to use the exact progression of steps above; the outline is simply a way to describe a systematic approach to problem solving. The remainder of this article provides you the opportunity to test your geometry skills by way of several practice problems. Obviously, these problems do not require you to go out and make any measurements of lengths or angles, but keep in mind that problems you encounter in everyday life may require you to do so!

Practice Problem : The floor plan of a house is shown below. Determine the area covered by the house.

Solution : Let's first divide the diagram of the house into two rectangles and a trapezoid, since we can calculate the area of each of these figures. Using the properties of each figure, we can also fill in some of the unknown information.

Now, the area of the larger rectangle is the product of 40 feet and 20 feet, or 800 square feet. The area of the smaller rectangle is 25 feet times 6 feet, or 150 square feet. The area of the trapezoid is the following:

The height ( h ) is 6 feet, and the two bases ( b 1 and b 2 ) are 8 and 11 feet.

Adding all three areas gives us a total area of the house of 1,007 square feet.

Practice Problem : A hiker is walking up a steep hill. The slope of the hill between two trees is constant, and the base of one tree is 100 meters higher than the other. If the horizontal distance between the trees is 400 meters, how far must the hiker walk to get from one tree to the next?

Solution : Because this problem may be difficult to envision, a diagram is extremely helpful. Notice that the base of the trees differ in height by 100 meters--this is our vertical distance for the walk. The horizontal distance is 400 meters.

Note that we have shown the right angle because horizontal and vertical segments are perpendicular. We can now use the Pythagorean theorem to calculate the distance d the hiker must walk.

Thus, the hiker must walk about 412 meters. Note that although the hiker makes a significant (100 meter) change in elevation over this walk, the difference between the actual distance he walks and the horizontal distance is small--only about 12 meters.

Practice Problem : A homeowner has a rectangular fenced-in yard, and he wants to put mulch on his triangular gardens, as shown below. The inside border of each garden always meets the fence at the same angle. If a bag of mulch covers about 50 square feet, how many bags of mulch should the homeowner buy to cover his gardens?

Solution : We are told in the problem that the inside border of each garden meets the fence at the same angle in every case; thus, we can conclude (as shown below) that the triangles are all isosceles (and that the triangles with the same side lengths are congruent by the ASA condition). We can thus mark each side with an unknown variable x or y .

Recall that the fenced-in area is rectangular; thus the angle in each corner is 90°. We can then solve for x and y using the Pythagorean theorem. Notice first, however, that x and y are the height and base of their respective triangles.

Because the gardens include two of each triangle shape, the total garden area is simply the sum of x 2 and y 2 . (If you do not follow this point, simply use the triangle area formula in each case--you will get the same result.)

Thus, the homeowner needs six bags of mulch (for a total of 300 square feet) to cover his gardens. (Of course, we are assuming here that he must buy a whole number of bags.)

• Course Catalog
• Group Discounts
• Gift Certificates
• For Libraries
• CEU Verification
• Medical Terminology
• Accounting Course
• Writing Basics
• QuickBooks Training
• Proofreading Class
• Sensitivity Training
• Excel Certificate
• Teach Online
• Terms of Service
• Privacy Policy

Open Omnia - Mathematics Solver with Steps

Geometry Math Problems - Perimeters

In these lessons, we will learn to solve geometry math problems that involve perimeter.

Related Pages Geometry math problems involving area Area Formula Geometry math problems involving angles More Algebra Word Problems

Geometry word problems involves geometric figures and angles described in words. You would need to be familiar with the formulas in geometry.

Making a sketch of the geometric figure is often helpful.

Geometry Word Problems Involving Perimeter

Example: A triangle has a perimeter of 50. If 2 of its sides are equal and the third side is 5 more than the equal sides, what is the length of the third side?

Solution: Step 1: Assign variables:

Let x = length of the equal sides Sketch the figure

Step 2: Write out the formula for perimeter of triangle .

P = sum of the three sides

Step 3: Plug in the values from the question and from the sketch.

50 = x + x + x+ 5

Combine like terms 50 = 3x + 5

Isolate variable x 3x = 50 – 5 3x = 45 x = 15

Be careful! The question requires the length of the third side.

The length of third side = 15 + 5 = 20

Answer: The length of third side is 20.

Geometry Math Problem involving the perimeter of a rectangle

The following two videos give the perimeter of a rectangle, a relationship between the length and width of the rectangle, and use that information to find the exact value of the length and width.

Example: A rectangular garden is 2.5 times as long as it is wide. It has a perimeter of 168 ft. How long and wide is the garden?

Example: A rectangular landing strip for an airplane has perimeter 8000 ft. If the length is 10 ft longer than 35 times the width, what is the length and width?

Examples of perimeter geometry word problems This video shows how to write an equation and find the dimensions of a rectangle knowing the perimeter and some information about the about the length and width.

Example: The width of a rectangle is 3 ft less than its length. The perimeter of the rectangle is 110 ft. Find the dimensions.

Perimeter Word Problems

Example: The length of a rectangle is 7 cm more than 4 times its width. Its perimeter is 124 cm. Find its dimensions.

Geometry Math Problem involving the perimeter of a triangle

The following two videos give the perimeter of a triangle, a relationship between the sides of the triangle, and use that information to find the exact value or values of the required side or sides.

Example: Patrick’s bike ride follows a triangular path; two legs are equal, the third is 8 miles longer than the other legs. If Patrick rides 30 miles total, what is the length of the longest leg?

Example: The perimeter of a triangle is 56 cm. The first side is 6 cm shorter than the second side. The third side is 2 cm shorter than twice the length of the first side. What is the length of each side?

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

• Math Lessons
• Math Formulas
• Calculators

Math Calculators, Lessons and Formulas

It is time to solve your math problem

• HW Help (paid service)
• Solving Equations
• Step-by-step Equation Solver

Step by step equation solver

This is an online calculator for solving algebraic equations. Simply enter the equation, and the calculator will walk you through the steps necessary to simplify and solve it. Each step is followed by a brief explanation.

• Factoring Polynomials
• Solving equations
• Rationalize Denominator
• Arithmetic sequences
• Polynomial Roots
• Synthetic Division
• Polynomial Operations
• Graphing Polynomials
• Simplify Polynomials
• Generate From Roots
• Simplify Expression
• Multiplication / Division
• Addition / Subtraction
• Simplifying
• Quadratic Equations Solver
• Polynomial Equations
• Solving Equations - With Steps
• Solving (with steps)
• Quadratic Plotter
• Factoring Trinomials
• Equilateral Triangle
• Right Triangle
• Oblique Triangle
• Square Calculator
• Rectangle Calculator
• Circle Calculator
• Hexagon Calculator
• Rhombus Calculator
• Trapezoid Calculator
• Triangular Prism
• Distance calculator
• Triangle Calculator
• Graphing Lines
• Lines Intersection
• Two Point Form
• Line-Point Distance
• Parallel/Perpendicular
• Circle Equation
• Circle From 3 Points
• Circle-line Intersection
• Modulus, inverse, polar form
• Vectors (2D & 3D)
• Add, Subtract, Multiply
• Determinant Calculator
• Matrix Inverse
• Characteristic Polynomial
• Eigenvalues
• Eigenvectors
• Matrix Decomposition
• Limit Calculator
• Derivative Calculator
• Integral Calculator
• Arithmetic Sequences
• Geometric Sequences
• Find n th Term
• Degrees to Radians
• Trig. Equations
• Long Division
• Evaluate Expressions
• Fraction Calculator
• Greatest Common Divisor GCD
• Least Common Multiple LCM
• Prime Factorization
• Scientific Notation
• Percentage Calculator
• Dec / Bin / Hex
• Probability Calculator
• Probability Distributions
• Descriptive Statistics
• Standard Deviation
• Z - score Calculator
• Normal Distribution
• T-Test Calculator
• Correlation & Regression
• Simple Interest
• Compound Interest
• Amortization Calculator
• Annuity Calculator
• Work Problems

Hire MATHPORTAL experts to do math homework for you.

Prices start at $3 per problem.

Related Calculators

Was this calculator helpful?

Please tell me how can I make this better.

Welcome to MathPortal. This website's owner is mathematician Miloš Petrović. I designed this website and wrote all the calculators, lessons, and formulas .

If you want to contact me, probably have some questions, write me using the contact form or email me on [email protected]

Email (optional)

15 Challenging Geometry Problems and Their Step-by-Step Solutions

• Author: Noreen Niazi
• Last Updated on: August 22, 2023

Introduction to Geometry Problems

The area of mathematics known as geometry is concerned with the study of the positions, dimensions, and shapes of objects.Geometry has applications in various fields, such as engineering, architecture, and physics. Geometry problems are among the most challenging and exciting problems in mathematics. Understanding and mastering geometry problems is essential for anyone who wants to pursue a career in any field requiring a good understanding of geometry.

Importance of Practicing Geometry Problems

Practicing geometry problems is essential for anyone who wants to master geometry. Geometry problems require a good understanding of the concepts, formulas, and theorems. By practicing geometry problems, you will develop a deep understanding of the concepts and the formulas.

You will also be able to identify the issues and the strategies to solve them. Practicing geometry problems will also help you to improve your problem-solving skills, which will be helpful in other areas of your life.

Types of Geometry Problems

There are several types of geometry problems. Some of the common types of geometry problems include:

• Congruence problems: These problems involve proving that two or more shapes are congruent.
• Similarity problems: These problems involve proving that two or more shapes are similar.
• Area and perimeter problems: These problems involve finding the area and perimeter of various shapes.
• Volume and surface area problems: These problems involve finding the volume and surface area of various shapes.
• Coordinate geometry problems: These problems involve finding the coordinates of various points on a graph.

Strategies for Solving Geometry Problems

To solve geometry problems, you must understand the concepts, formulas, and theorems well. You also need to have a systematic approach to solving problems. Some of the strategies for solving geometry problems include:

• Read the problem carefully: You must read the situation carefully and understand what is required.
• Draw a diagram: You need to draw a diagram representing the problem. This will help you to visualize the problem and identify the relationships between the shapes.
• Identify the type of problem: You need to identify the problem type and the applicable formulas and theorems.
• Solve the problem step by step: You need to solve the problem step by step, showing all your work.
• Check your answer: You must check it to ensure it is correct.

Common Geometry Formulas and Theorems

To solve geometry problems, you must understand the standard formulas and theorems well. Some of the common procedures and theorems include:

• Area of a square: side × side.
• Pythagoras theorem: a² + b² = c², where a and b are the lengths of the two sides of a right-angled triangle, and c is the hypotenuse length.
• Area of a rectangle: length × breadth.
• Circumference of a circle : 2 × π × radius.
• Area of a triangle : ½ × base × height.
• Congruent triangles theorem: Triangles are congruent if they have the same shape and size.
• Area of a circle: π × radius².
• Similar triangles theorem: Triangles are similar if they have the same shape but different sizes.

Problem 1: Lets the length of three sides of triangle be 3 cm, 4 cm, and 5 cm. Calculate the area of a right-angled triangle.

Using the Pythagoras theorem:

$$a² + b² = c²$$

where a = 3 cm, b = 4 cm, and c = 5 cm.

$$3² + 4² = 5²$$

$$9 + 16 = 25$$

Therefore, $$c² = 25$$, and $$c = √25 = 5 cm$$.

• The area of the triangle = $$½ × \text{base} × \text{height}$$ 

$$= ½ × 3 cm × 4 cm $$

$$= 6 cm².$$

Problem 2:If the length of each side of an equilateral triangle is 10 cm then calculate its perimeter.

As the perimeter of an equilateral triangle = $$3 × side length.$$

• Therefore, the perimeter of the triangle $$= 3 × 10 cm = 30 cm.$$

Problem 3: If cylinder has 4cm radius and 10 cm height then what is the volume of a cylinder.

The volume of a cylinder = $$π × radius² × height.$$

• Therefore, the volume of the cylinder $$= π × 4² × 10 cm = 160π cm³$$.

Problem 4: If radius of a circle is given by 5cm and central angle 60° then what is the area of sector of a circle.

The area of a sector of a circle $$= (central angle ÷ 360°) × π × radius².$$

• Therefore, the area of the sector $$= (60° ÷ 360°) × π × 5² c = 4.36 cm².$$

Problem 5: Find the hypotenuse of right-angled triangle, if its other two sides are of 8 cm and 15 cm.

Using the Pythagoras theorem :

Where a = 8 cm, b = 15 cm , and c is the hypotenuse length.

$$8² + 15² = c²$$

$$64 + 225 = c²$$

• Therefore, $$c² = 289,$$ and $$c = √289 = 17 cm.$$

Problem 6: If two parallel sides of trapezium are of length 5 cm and 10 cm and height 8 cm. Calculate the area of a trapezium.

The area of a trapezium = $$½ × (sum of parallel sides) × height.$$

• Therefore, the area of the trapezium $$= ½ × (5 cm + 10 cm) × 8 cm = 60 cm².$$

Problem 7: Radius and height of cone is given by 6cm and 12 cm respectively. Calculate its volume.

The volume of a cone $$= ⅓ × π × radius² × height.$$

• Therefore, the volume of the cone $$= ⅓ × π × 6² × 12 cm³ = 452.39 cm³.$$

Problem 8:What is the length of side of square if its area is 64 cm².

The area of a square $$= side × side.$$

• Therefore, $$side = √64 cm = 8 cm.$$

Problem 9: If length rectangle is 10cm and breadth is 6cm. Calculate its diagonal.

Where $$a = 10 cm$$, $$b = 6 cm$$, and c is the diagonal length.

$$10² + 6² = c²$$

$$100 + 36 = c²$$

• Therefore, $$c² = 136,$$ and $$c = √136 cm = 11.66 cm.$$

Problem 10: If one side of regular hexagon is of 8cm then what is the area of a regular hexagon.

The area of a regular hexagon $$= 6 × (side length)² × (√3 ÷ 4).$$

• Therefore, the area of the hexagon $$= 6 × 8² × (√3 ÷ 4) cm² = 96√3 cm².$$

Problem 11: If radius of sphere is 7 cm, then what is its volume.

The volume of a sphere = $$⅔ × π × radius³.$$

• Therefore, the volume of the sphere $$= ⅔ × π × 7³ cm³ = 1436.76 cm³.$$

Problem 12: Find the hypotenuse length of a right-angled triangle with sides of 6 cm and 8 cm.

Where a = 6 cm, b = 8 cm, and c is the hypotenuse length.

$$6² + 8² = c²$$

$$36 + 64 = c²$$

Therefore, $$c² = 100,$$ and $$c = √100 cm = 10 cm.$$

Problem 13: Find the area of a rhombus with 12 cm and 16 cm diagonals.

The area of a rhombus = (diagonal 1 × diagonal 2) ÷ 2.

• Therefore, the area of the rhombus = (12 cm × 16 cm) ÷ 2 = 96 cm².

Problem 14: If radius and central angle of circle is 4cm and 45° respectively then what is the length oof arc of circle.

The length of the arc of a circle = (central angle ÷ 360°) × 2 × π × radius.

• Therefore, the length of the arc = (45° ÷ 360°) × 2 × π × 4 cm

Problem 15: Find the length of the side of a regular octagon with the radius of the inscribed circle measuring 4 cm.

The length of the side of a regular octagon = (radius of the inscribed circle) × √2.

Therefore, the length of the side of the octagon = 4 cm × √2 

Online Resources for Geometry Practice Problems

There are several online resources that you can use to practice geometry problems. Some of the popular online resources include:

• Khan Academy : On the free online learning platform Khan Academy, you may find practise questions and video lectures on a variety of subjects, including geometry.
• Mathway : Mathway is an online tool that can solve various math problems, including geometry problems.
• IXL :IXL is a website that provides practise questions and tests on a variety of subjects, including geometry.

Q: What is geometry?

A: Geometry is the branch of mathematics that studies objects’ shapes, sizes, and positions.

Q: Why is practicing geometry problems significant?

A: Practicing geometry problems is essential for anyone who wants to master geometry. Geometry problems require a good understanding of the concepts, formulas, and theorems. By practicing geometry problems, you will develop a deep understanding of the concepts and the formulas.

Q: What are some standard geometry formulas and theorems?

A: Some of the standard geometry formulas and theorems include the Pythagoras theorem, area of a triangle, area of a square, area of a rectangle, area of a circle, circumference of a circle, congruent triangles theorem, and similar triangles theorem.

Geometry problems are among the most challenging and exciting problems in mathematics. Understanding and mastering geometry problems is essential for anyone who wants to pursue a career in any field requiring a good understanding of geometry. By practicing geometry problems and using the strategies and formulas discussed in this article, you can master geometry and improve your problem-solving skills.

• Math Tutorials
• Trigonometry
• Cookie Policy
• Privacy Policy and Terms of Use

Connect With Us

• LearnAboutMath Newsletter

The Best Math Website for Learning and Practice

By signing up you are agreeing to receive emails according to our privacy policy.

Stay tuned with our latest math posts

High Impact Tutoring Built By Math Experts

Personalized standards-aligned one-on-one math tutoring for schools and districts

Free ready-to-use math resources

Hundreds of free math resources created by experienced math teachers to save time, build engagement and accelerate growth

20 Effective Math Strategies To Approach Problem-Solving 

Katie Keeton

Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems.  

Problem-solving skills are essential to math in the general classroom and real-life. They require logical reasoning and critical thinking skills. Students must be equipped with strategies to help them find solutions to problems.

This article explores mathematical problem solving strategies, logical reasoning and critical thinking skills to help learners with solving math word problems independently in real-life situations. 

What are problem-solving strategies?

Problem-solving strategies in math are methods students can use to figure out solutions to math problems. Some problem-solving strategies: 

• Draw a model
• Use different approaches
• Check the inverse to make sure the answer is correct

Students need to have a toolkit of math problem-solving strategies at their disposal to provide different ways to approach math problems. This makes it easier to find solutions and understand math better. 

Strategies can help guide students to the solution when it is difficult ot know when to start.

The ultimate guide to problem solving techniques

Download these ready-to-go problem solving techniques that every student should know. Includes printable tasks for students including challenges, short explanations for teachers with questioning prompts.

20 Math Strategies For Problem-Solving

Different problem-solving math strategies are required for different parts of the problem. It is unlikely that students will use the same strategy to understand and solve the problem. 

Here are 20 strategies to help students develop their problem-solving skills. 

Strategies to understand the problem

Strategies that help students understand the problem before solving it helps ensure they understand: 

• The context
• What the key information is
• How to form a plan to solve it

Following these steps leads students to the correct solution and makes the math word problem easier .

Here are five strategies to help students understand the content of the problem and identify key information. 

1. Read the problem aloud

Read a word problem aloud to help understand it. Hearing the words engages auditory processing. This can make it easier to process and comprehend the context of the situation.

2. Highlight keywords 

When keywords are highlighted in a word problem, it helps the student focus on the essential information needed to solve it. Some important keywords help determine which operation is needed.  For example, if the word problem asks how many are left, the problem likely requires subtraction.  Ensure students highlight the keywords carefully and do not highlight every number or keyword. There is likely irrelevant information in the word problem.

3. Summarize the information

Read the problem aloud, highlight the key information and then summarize the information. Students can do this in their heads or write down a quick summary.  Summaries should include only the important information and be in simple terms that help contextualize the problem.

4. Determine the unknown

A common problem that students have when solving a word problem is misunderstanding what they are solving. Determine what the unknown information is before finding the answer.  Often, a word problem contains a question where you can find the unknown information you need to solve. For example, in the question ‘How many apples are left?’ students need to find the number of apples left over.

5. Make a plan

Once students understand the context of the word problem, have dentified the important information and determined the unknown, they can make a plan to solve it.  The plan will depend on the type of problem. Some problems involve more than one step to solve them as some require more than one answer.  Encourage students to make a list of each step they need to take to solve the problem before getting started.

Strategies for solving the problem 

1. draw a model or diagram.

Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process.  It can help to visualize the problem to understand the relationships between the numbers in the problem. In turn, this helps students see the solution.

Similarly, you could draw a model to represent the objects in the problem:

2. Act it out

This particular strategy is applicable at any grade level but is especially helpful in math investigation in elementary school . It involves a physical demonstration or students acting out the problem using movements, concrete resources and math manipulatives .  When students act out a problem, they can visualize and contectualize the word problem in another way and secure an understanding of the math concepts.  The examples below show how 1st-grade students could “act out” an addition and subtraction problem:

3. Work backwards

Working backwards is a popular problem-solving strategy. It involves starting with a possible solution and deciding what steps to take to arrive at that solution.  This strategy can be particularly helpful when students solve math word problems involving multiple steps. They can start at the end and think carefully about each step taken as opposed to jumping to the end of the problem and missing steps in between.

For example,

To solve this problem working backwards, start with the final condition, which is Sam’s grandmother’s age (71) and work backwards to find Sam’s age. Subtract 20 from the grandmother’s age, which is 71.  Then, divide the result by 3 to get Sam’s age. 71 – 20 = 51 51 ÷ 3 = 17 Sam is 17 years old.

4. Write a number sentence

When faced with a word problem, encourage students to write a number sentence based on the information. This helps translate the information in the word problem into a math equation or expression, which is more easily solved.  It is important to fully understand the context of the word problem and what students need to solve before writing an equation to represent it.

5. Use a formula

Specific formulas help solve many math problems. For example, if a problem asks students to find the area of a rug, they would use the area formula (area = length × width) to solve.   Make sure students know the important mathematical formulas they will need in tests and real-life. It can help to display these around the classroom or, for those who need more support, on students’ desks.

Strategies for checking the solution 

Once the problem is solved using an appropriate strategy, it is equally important to check the solution to ensure it is correct and makes sense. 

There are many strategies to check the solution. The strategy for a specific problem is dependent on the problem type and math content involved.

Here are five strategies to help students check their solutions. 

1. Use the Inverse Operation

For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7. As good practice, encourage students to use the inverse operation routinely to check their work. 

2. Estimate to check for reasonableness

Once students reach an answer, they can use estimation or rounding to see if the answer is reasonable.  Round each number in the equation to a number that’s close and easy to work with, usually a multiple of ten.  For example, if the question was 216 ÷ 18 and the quotient was 12, students might round 216 to 200 and round 18 to 20. Then use mental math to solve 200 ÷ 20, which is 10.  When the estimate is clear the two numbers are close. This means your answer is reasonable. 

3. Plug-In Method

This method is particularly useful for algebraic equations. Specifically when working with variables.  To use the plug-in method, students solve the problem as asked and arrive at an answer. They can then plug the answer into the original equation to see if it works. If it does, the answer is correct.

If students use the equation 20m+80=300 to solve this problem and find that m = 11, they can plug that value back into the equation to see if it is correct. 20m + 80 = 300 20 (11) + 80 = 300 220 + 80 = 300 300 = 300 ✓

4. Peer Review

Peer review is a great tool to use at any grade level as it promotes critical thinking and collaboration between students. The reviewers can look at the problem from a different view as they check to see if the problem was solved correctly.   Problem solvers receive immediate feedback and the opportunity to discuss their thinking with their peers. This strategy is effective with mixed-ability partners or similar-ability partners. In mixed-ability groups, the partner with stronger skills provides guidance and support to the partner with weaker skills, while reinforcing their own understanding of the content and communication skills.  If partners have comparable ability levels and problem-solving skills, they may find that they approach problems differently or have unique insights to offer each other about the problem-solving process.

5. Use a Calculator

A calculator can be introduced at any grade level but may be best for older students who already have a foundational understanding of basic math operations. Provide students with a calculator to allow them to check their solutions independently, accurately, and quickly. Since calculators are so readily available on smartphones and tablets, they allow students to develop practical skills that apply to real-world situations.  

Step-by-step problem-solving processes for your classroom

In his book, How to Solve It , published in 1945, mathematician George Polya introduced a 4-step process to solve problems. 

Polya’s 4 steps include:

• Understand the problem
• Devise a plan
• Carry out the plan

Today, in the style of George Polya, many problem-solving strategies use various acronyms and steps to help students recall. 

Many teachers create posters and anchor charts of their chosen process to display in their classrooms. They can be implemented in any elementary, middle school or high school classroom. 

Here are 5 problem-solving strategies to introduce to students and use in the classroom.

How Third Space Learning improves problem-solving 

Resources .

Third Space Learning offers a free resource library is filled with hundreds of high-quality resources. A team of experienced math experts carefully created each resource to develop students mental arithmetic, problem solving and critical thinking. 

Explore the range of problem solving resources for 2nd to 8th grade students. 

One-on-one tutoring 

Third Space Learning offers one-on-one math tutoring to help students improve their math skills. Highly qualified tutors deliver high-quality lessons aligned to state standards. 

Former teachers and math experts write all of Third Space Learning’s tutoring lessons. Expertly designed lessons follow a “my turn, follow me, your turn” pedagogy to help students move from guided instruction and problem-solving to independent practice. 

Throughout each lesson, tutors ask higher-level thinking questions to promote critical thinking and ensure students are developing a deep understanding of the content and problem-solving skills.

Problem-solving

Educators can use many different strategies to teach problem-solving and help students develop and carry out a plan when solving math problems. Incorporate these math strategies into any math program and use them with a variety of math concepts, from whole numbers and fractions to algebra. 

Teaching students how to choose and implement problem-solving strategies helps them develop mathematical reasoning skills and critical thinking they can apply to real-life problem-solving.

READ MORE : 8 Common Core math examples

There are many different strategies for problem-solving; Here are 5 problem-solving strategies: • draw a model  • act it out  • work backwards  • write a number sentence • use a formula

Here are 10 strategies of problem-solving: • Read the problem aloud • Highlight keywords • Summarize the information • Determine the unknown • Make a plan • Draw a model  • Act it out  • Work backwards  • Write a number sentence • Use a formula

1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back

Some strategies you can use to solve challenging math problems are: breaking the problem into smaller parts, using diagrams or models, applying logical reasoning, and trying different approaches.

Related articles

Why Student Centered Learning Is Important: A Guide For Educators

13 Effective Learning Strategies: A Guide to Using them in your Math Classroom

Differentiated Instruction: 9 Differentiated Curriculum And Instruction Strategies For Teachers 

5 Math Mastery Strategies To Incorporate Into Your 4th and 5th Grade Classrooms

Ultimate Guide to Metacognition [FREE]

Looking for a summary on metacognition in relation to math teaching and learning?

Check out this guide featuring practical examples, tips and strategies to successfully embed metacognition across your school to accelerate math growth.

Privacy Overview

Game Central

Similar problems from web search.

Advertisement

BrainTwister #18: The arithmetical two‑step

Can you solve this week’s logic puzzle? Plus our quick quiz and the answer to last week’s problem

By Peter Rowlett

Shutterstock/ktsdesign

#18 The arithmetical two-step

Set by Peter Rowlett

You must take two steps to get from a given number to make 10. Each step must change the number by adding, subtracting, multiplying by or dividing by a number from 1 to 9. (Multiplying or dividing by 1 isn’t allowed as it doesn’t change the number.)

For example, starting with 35, one way would be to first divide by 7 then add 5.

Can you take two steps to get from 42 to 10?

Is it possible to get to 10 in two steps from all the numbers 11 to 30?…

Sign up to our weekly newsletter

Receive a weekly dose of discovery in your inbox! We'll also keep you up to date with New Scientist events and special offers.

To continue reading, subscribe today with our introductory offers

No commitment, cancel anytime*

Offer ends 2nd of July 2024.

*Cancel anytime within 14 days of payment to receive a refund on unserved issues.

Inclusive of applicable taxes (VAT)

Existing subscribers

More from New Scientist

Explore the latest news, articles and features

Protocells on early Earth may have been formed by squeezing geysers

Subscriber-only

Flies undertake epic migrations that may be vital for pollination

China is sending its chang’e 6 spacecraft to the far side of the moon, mysterious space signals may come from a dead star with a planet, popular articles.

Trending New Scientist articles

LSAT AI - Scan & Solve Prep 4+

Solver to study for the lsat, cuff media group llc, designed for ipad.

• Offers In-App Purchases

Screenshots

Description.

Solve any LSAT problem on the go with LSAT AI, your dedicated step-by-step LSAT solver app! Facing a tough LSAT question? Seeking instant, detailed explanations? LSAT AI is your go-to solution. Whether it's multiple-choice, passage-based, or standalone questions, LSAT AI has got your back. Just upload or snap a photo of your LSAT question, and LSAT AI instantly identifies the problem, offering you a comprehensive explanation on how to solve it. KEY FEATURES Upload or take a photo of any handwritten or digital LSAT question. Copy and share in-depth solutions. Covers all LSAT subjects, including arguments, logic games, reading comprehension, flawed reasoning, parallel reasoning, inference questions, and more! Detailed explanations and reasoning provided for each solution. Try our app with a free trial and see the difference in your preparation. You must have an active subscription to access LSAT AI. We offer an annual subscription and a weekly subscription, which includes a 3-day free trial. Experience the app without charge for 3 days with the trial, after which the billing cycle begins. Subscriptions can be canceled anytime under your App Subscription management in Settings. By utilizing LSAT AI, you agree to our Terms of Use and Privacy Policy. Terms of use: https://cuffmediagroup.com/terms-conditions Privacy Policy: https://cuffmediagroup.com/privacy-policy

App Privacy

The developer, Cuff Media Group LLC , indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy .

Data Used to Track You

The following data may be used to track you across apps and websites owned by other companies:

• User Content

Data Linked to You

The following data may be collected and linked to your identity:

Data Not Linked to You

The following data may be collected but it is not linked to your identity:

• Diagnostics

Privacy practices may vary, for example, based on the features you use or your age. Learn More

Information

• LSAT Answers - Weekly Sub $4.99
• LSAT AI Answers - Yearly Sub $34.99
• App Support
• Privacy Policy

More By This Developer

Cuff: Video Chat, Make Friends

Chem AI: Chemistry Solver

LevelUp - Create Pro Headshots

Physics AI - Physics Solver

Stylist - Hairstyle Try On

Solver Title

Generating PDF...

• Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Expanded Form Mean, Median & Mode
• Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Logical Sets Word Problems
• Pre Calculus Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry
• Calculus Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform
• Functions Line Equations Functions Arithmetic & Comp. Conic Sections Transformation
• Linear Algebra Matrices Vectors
• Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
• Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution
• Physics Mechanics
• Chemistry Chemical Reactions Chemical Properties
• Finance Simple Interest Compound Interest Present Value Future Value
• Economics Point of Diminishing Return
• Conversions Roman Numerals Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time Volume
• Pre Algebra
• One-Step Addition
• One-Step Subtraction
• One-Step Multiplication
• One-Step Division
• One-Step Decimals
• Two-Step Integers
• Two-Step Add/Subtract
• Two-Step Multiply/Divide
• Two-Step Fractions
• Two-Step Decimals
• Multi-Step Integers
• Multi-Step with Parentheses
• Multi-Step Rational
• Multi-Step Fractions
• Multi-Step Decimals
• Solve by Factoring
• Completing the Square
• Quadratic Formula
• Biquadratic
• Logarithmic
• Exponential
• Rational Roots
• Floor/Ceiling
• Equation Given Roots
• Newton Raphson
• Substitution
• Elimination
• Cramer's Rule
• Gaussian Elimination
• System of Inequalities
• Perfect Squares
• Difference of Squares
• Difference of Cubes
• Sum of Cubes
• Polynomials
• Distributive Property
• FOIL method
• Perfect Cubes
• Binomial Expansion
• Negative Rule
• Product Rule
• Quotient Rule
• Expand Power Rule
• Fraction Exponent
• Exponent Rules
• Exponential Form
• Logarithmic Form
• Absolute Value
• Rational Number
• Powers of i
• Complex Form
• Partial Fractions
• Is Polynomial
• Leading Coefficient
• Leading Term
• Standard Form
• Complete the Square
• Synthetic Division
• Linear Factors
• Rationalize Denominator
• Rationalize Numerator
• Identify Type
• Convergence
• Interval Notation
• Pi (Product) Notation
• Boolean Algebra
• Truth Table
• Mutual Exclusive
• Cardinality
• Caretesian Product
• Age Problems
• Distance Problems
• Cost Problems
• Investment Problems
• Number Problems
• Percent Problems
• Addition/Subtraction
• Multiplication/Division
• Dice Problems
• Coin Problems
• Card Problems
• Pre Calculus
• Linear Algebra
• Trigonometry
• Conversions

Most Used Actions

Number line.

• -x+3\gt 2x+1
• (x+5)(x-5)\gt 0
• 10^{1-x}=10^4
• \sqrt{3+x}=-2
• 6+11x+6x^2+x^3=0
• factor\:x^{2}-5x+6
• simplify\:\frac{2}{3}-\frac{3}{2}+\frac{1}{4}
• x+2y=2x-5,\:x-y=3
• How do you solve algebraic expressions?
• To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations. Then, solve the equation by finding the value of the variable that makes the equation true.
• What are the basics of algebra?
• The basics of algebra are the commutative, associative, and distributive laws.
• What are the 3 rules of algebra?
• The basic rules of algebra are the commutative, associative, and distributive laws.
• What is the golden rule of algebra?
• The golden rule of algebra states Do unto one side of the equation what you do to others. Meaning, whatever operation is being used on one side of equation, the same will be used on the other side too.
• What are the 5 basic laws of algebra?
• The basic laws of algebra are the Commutative Law For Addition, Commutative Law For Multiplication, Associative Law For Addition, Associative Law For Multiplication, and the Distributive Law.

algebra-calculator

• High School Math Solutions – Systems of Equations Calculator, Elimination A system of equations is a collection of two or more equations with the same set of variables. In this blog post,...

Please add a message.

Message received. Thanks for the feedback.

Annual skilled trades competition builds technical and professional skills for Iowa students

• Wednesday, May 1, 2024
• Headline Story

Southeast Polk senior Simon Frohock (R) competed in the cabinet making contest for a second year.

High-quality career and professional skill development took center stage last week as over 600 high school and college students took part in the annual SkillsUSA State Leadership and Skills Conference . Held in Ankeny at the Des Moines Area Community College campus, this two-day competition featured over 50 different leadership and technical competitions for students to test their technical skills and knowledge, explore career pathways and make valuable connections with local industry leaders.

Southeast Polk High School seniors Delvis Kouete and Simon Frohock, both 17, were well-prepared for the competition, which featured timed activities related to industrial technology, carpentry, robotics, automotive repair and job interview techniques, among many others. For this year’s skills competition, Delvis competed in architectural drafting and was a member of the school’s quiz bowl team. Simon, the 2023 state champion in cabinet making, returned for a second year in the cabinet making contest. Both students competed well in their individual competitions, with Delvis placing fifth and Simon serving as this year’s runner-up.

“The skills competition can help you strive for excellence in your work and learning,” Simon said. “Even though it’s a competition and there is pressure to do well, it’s a good, low-risk way to see what an employee in this work has to do every day.”

Both Simon and Delvis noted that the competition not only helps to strengthen a student’s technical skills, but it also engages students in career pathway discovery and professional skill development.

“Being a part of SkillsUSA and competing in the skills competition has helped me learn new skills with my hands and work on teamwork, communication and leadership skills,” Delvis said. “You learn how to work with other people that aren’t like you and get your mind thinking about your future career.”

Along with the individual contests, all competitors at the SkillsUSA State Leadership and Skills Conference were required to submit a resume and take a professional development test that focused on workplace, professional and technical skills as well as overall knowledge of SkillsUSA.

“SkillsUSA helps provide real-world context to the content being taught by classroom educators,” said Kent Storm, state director for SkillsUSA Iowa. “Taking the learning beyond the classroom allows students to grow and learn next to industry partners and gain valuable experience."

As one of Iowa’s career and technical student organizations (CTSO) , SkillsUSA champions the skilled trades industry and provides opportunities for students to apply the skills they have developed in classrooms through conferences, competitions, community service events, worksite visits and other activities.

“Participation in a CTSO like SkillsUSA helps students gain hands-on experience and connect classroom curricula to careers,” said Cale Hutchings, education consultant at the Iowa Department of Education. “Through CTSOs, students can become leaders and strengthen their employability skills, which is valuable as they explore potential next steps in their college and career pathways.”

SkillsUSA boasts a roster of over 400,000 members nationwide. In Iowa, over 1,300 students and advisers in career and technical education programs participate in local SkillsUSA chapters.

At Southeast Polk, 21 student members are a part of their SkillsUSA chapter. Led by industrial technology teachers and chapter advisers Ryan Andersen and Brett Rickabaugh, the students have been involved with several community service projects, employer presentations and opportunities to work closely with instructors.

“Any time a student participates in SkillsUSA, it gives us more time with that student to elaborate on what we’ve learned in class,” Andersen said. “They can connect the idea to the planning, design and completion of a project and how that activity fits into a real career. That’s something we can’t replicate without a CTSO.”

Anderson also stated that students who participate in SkillsUSA and activities like the State Leadership and Skills Conference build confidence through their experiences.

“It really helps students to have the confidence to rely on their skills and what they know,” he said. “The skills competition requires them to use problem-solving skills and build off their knowledge to continue to learn and persevere.”

This year’s first-place winners at the SkillsUSA State Leadership and Skills Conference will move onward to compete with 6,000 other students at the national conference in Atlanta this June.

For Simon and Delvis, the skills competition was another step in building necessary skills and acumen for their futures. Simon, with his penchant for cabinet making, already has a full-time job lined up after graduation with a local cabinet shop. Additionally, Delvis would like to pursue something within the computer science field, perhaps in the coding or software engineering areas, and although he is changing fields, he believes SkillsUSA has helped him feel more prepared for the future.

“It has definitely helped me with skill-building and problem-solving,” he said. “What I’ve learned will be beneficial no matter what I decide to do next.”