Perimeter, Area, and Volume: Lesson 3 - Perimeter and Circumference

Perimeter and Circumference is the third of seven self-paced lessons in the “Perimeter, Area, and Volume” section of KET’s GED^{®} Geometry Professional Development Online Course. This lesson focuses on finding the exterior dimensions of a plane figure.

NOTE: This course was created based on the 2002 GED^{®} math test. The geometry instruction in this course is still valid, however, for up-to-date information about the 2014 GED^{®} math test, please visit KET’s GED^{®} Test Info: Mathematics online course.

On the GED^{®} Mathematics Test, students will apply their understanding of plane figures to solving problems.

They will need to find the perimeter of a square, rectangle, or triangle by adding sides or by using a provided formula.

They also need to know how to find the circumference of a circle.

This lesson focuses on finding the exterior dimensions of a plane figure. On the GED Mathematics Test, students may need to recognize a plane figure in a realistic context and to either select the correct formula from the formulas page or simply add the sides.

Note: Based on the GED formulas page, use the value of π in the decimal form, 3.14.

2Perimeter

Perimeter is the measure of the distance around the boundary of an object or figure.

To find the perimeter, you can always add the lengths of the sides. Formulas for perimeters are shortcuts for adding the lengths, and they can be found on the GED formulas page.

Question The Evans family needs to install a fence to enclose their swimming pool. The pool area that needs fencing is 40 feet long and 25 feet wide. How many feet of fencing do they need?

Step 1 Sketch the shape of the pool area. Label the length of the rectangle 40 feet and the width 25 feet.

Step 2 Choose the formula to find the perimeter.

rectangle Perimeter = 2 × length + 2 × width

Step 3 Substitute the length and width measurements from the problem into the formula.

Perimeter = 2 × length + 2 × width

= (2 × 40) + (2 × 25)

= 80 + 50

= 130

Answer 130 feet

3Circumference

Watch the video for an explanation of finding the circumference of a circle.

Pi, Circumference, and Radius

Video: 1m 15s

The distance around a circle is the circumference. The formula for circumference, shown below, is on the GED formulas page.

Circumference = π × diameter

π is approximately equal to 3.14

The number pi (Greek letter π) comes from the discovery that the circumference of a circle is always a little larger than three times a circle’s diameter. We can use pi to find the circumference of any circle.

A circle’s diameter is always twice the length of its radius.

Question Denise walks around a pond in the park every morning. The pond has a radius of 150 yards. How far does she go on her morning walk, in yards?

Step 1 Reread the problem to find the radius of the pond.

The radius is 150 yards.

Step 2 Find the diameter of the pond by multiplying the radius by 2.

150 × 2 = 300

Step 3 Substitute the measure of the diameter into the circumference formula, and solve.

Circumference = π × diameter

= 3.14 × diameter

= 3.14 × 300

= 942

Answer 942 yards

4Sample GED Questions

Directions: There are two questions on this page. Each will appear in the blue rectangle below. Click on Question 1 to see the first question, and then select your answer. Click on Question 2 to see the second question, and select your answer. As you solve these problems, consider how you would work through them with your students.

How could you help students choose the correct formula for Question 1?

Perimeter, Area, and Volume: Perimeter and Circumference Skill Review

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Printable Resource

In this lesson you have learned about perimeter and circumference. This review consists of key terms and concepts with which you will need to be familiar. Click the view button on the left to access a review sheet.

Below you will also see a Classroom Connection with suggestions for linking this geometry content with your instruction.