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Perimeter Unit 1 > Lesson 1 of 8

The perimeter of a polygon is the distance around the outside of the polygon. A polygon is 2-dimensional; however, perimeter is 1-dimensional and is measured in linear units. To help us make this distinction, look at our picture of a rectangular backyard. The yard is 2-dimensional: it has a length and a width. The amount of fence needed to enclose the backyard (perimeter) is 1-dimensional. The perimeter of this yard is the distance around the outside of the yard, indicated by the red arrow; It is measured in linear units such as feet or meters. [IMAGE]
To find the perimeter of a polygon, take the sum of the length of each side. The polygons below are much smaller than a fenced-in yard. Thus, we use smaller units in our examples, such as centimeters and inches.

Example 1: Find the perimeter of a triangle with sides measuring 5 centimeters, 9 centimeters and 11 centimeters. [IMAGE]
Solution: P = 5 cm + 9 cm + 11 cm = 25 cm

Example 2: A rectangle has a length of 8 centimeters and a width of 3 centimeters. Find the perimeter. [IMAGE]
Solution 1: P = 8 cm + 8cm + 3 cm + 3 cm = 22 cm
Solution 2: P = 2(8 cm) + 2(3 cm) = 16 cm + 6 cm = 22 cm

In Example 2, the second solution is more commonly used. In fact, in mathematics, we commonly use the following formula for perimeter of a rectangle:

P = 2L + 2W,  where P is the perimeter, L is the length and W is the width.
In the next few examples, we will find the perimeter of other polygons.

Example 3: Find the perimeter of a square with each side measuring 2 inches. [IMAGE]
Solution: P = 2 in + 2 in + 2 in + 2 in = 8 in

Example 4: Find the perimeter of an equilateral triangle with each side measuring 4 centimeters. [IMAGE]
Solution: P = 4 cm + 4 cm + 4 cm = 12 cm

A square and an equilateral triangle are both examples of regular polygons. Another method for finding the perimeter of a regular polygon is to multiply the number of sides by the length of one side. Let's revisit Examples 3 and 4 using this second method.

Example 3: Find the perimeter of a square with each side measuring 2 inches. [IMAGE]
Solution: This regular polygon has 4 sides, each with a length of 2 inches. Thus we get:
  P = 4(2 in) = 8 in

Example 4: Find the perimeter of an equilateral triangle with each side measuring 4 centimeters. [IMAGE]
Solution: This regular polygon has 3 sides, each with a length of 4 centimeters. Thus we get:
  P = 3(4 cm) = 12 cm

Example 5: Find the perimeter of a regular pentagon with each side measuring 3 inches. [IMAGE]
Solution: P = 5(3 in) = 15 in

Example 6: The perimeter of a regular hexagon is 18 centimeters. How long is one side? [IMAGE]
Solution: P = 18 cm
  Let s represent the length of one side. A regular hexagon has 6 sides, so we can divide the perimeter by 6 to get the length of one side (s).
  s = 18 cm ÷ 6
  s = 3 cm

Summary: To find the perimeter of a polygon, take the sum of the length of each side. The formula for perimeter of a rectangle is: P = 2L + 2W. To find the perimeter of a regular polygon, multiply the number of sides by the length of one side.


Exercises

Directions: Read each question below. Click once in an ANSWER BOX and type in your answer; then click ENTER. Your answers should be given as whole numbers greater than zero. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

1. Find the perimeter of a triangle with sides measuring 10 inches, 14 inches and 15 inches.
ANSWER BOX:  P = in

RESULTS BOX:


2. A rectangle has a length of 12 centimeters and a width of 4 centimeters. Find the perimeter.
ANSWER BOX:  P = cm

RESULTS BOX:


3. Find the perimeter of a regular hexagon with each side measuring 8 meters.
ANSWER BOX:  P = m

RESULTS BOX:


4. The perimeter of a square is 20 feet. How long is each side?
ANSWER BOX:  s = ft

RESULTS BOX:


5. The perimeter of a regular pentagon is 100 centimeters. How long is each side?
ANSWER BOX:  s = cm

RESULTS BOX:



This lesson is by Gisele Glosser. You can find me on Google.

Perimeter & Area Unit
Perimeter of Polygons
Area of Rectangles
Area of Parallelograms
Area of Triangles
Area of Trapezoids
Practice Exercises
Challenge Exercises
Solutions

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