Perimeter of a Triangle, Perimeter of a Rectangle, and Other Polygons

Learn About Perimeter of Triangles, Perimeter of Rectangles, and Other Polygons With The Following Examples And Interactive Exercises

Perimeter and Area of Polygons

Perimeter and Area of PolygonsThe 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.

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.


scalene triangleExample 1: Find the perimeter of a triangle with sides measuring 5 centimeters, 9 centimeters and 11 centimeters.

Solution: P = 5 cm + 9 cm + 11 cm = 25 cm


rectangleExample 2: A rectangle has a length of 8 centimeters and a width of 3 centimeters. Find the perimeter.

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:

perimeter formula where p_0.gif is the perimeter, l.gif is the length and w.gif is the width.

In the next few examples, we will find the perimeter of other polygons.


squareExample 3: Find the perimeter of a square with each side measuring 2 inches.

Solution: p.gif = 2 in + 2 in + 2 in + 2 in = 8 in


equilateral triangleExample 4: Find the perimeter of an equilateral triangle with each side measuring 4 centimeters.

Solution: p.gif = 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.


squareExample 3: Find the perimeter of a square with each side measuring 2 inches.

Solution: This regular polygon has 4 sides, each with a length of 2 inches. Thus we get:

p.gif = 4(2 in) = 8 in


equilateral triangleExample 4: Find the perimeter of an equilateral triangle with each side measuring 4 centimeters.

Solution: This regular polygon has 3 sides, each with a length of 4 centimeters. Thus we get:

p.gif = 3(4 cm) = 12 cm


pentagonExample 5: Find the perimeter of a regular pentagon with each side measuring 3 inches.

Solution: p.gif = 5(3 in) = 15 in


regular hexagonExample 6: The perimeter of a regular hexagon is 18 centimeters. How long is one side?

Solution: p.gif = 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: perimeter_formula. 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_0.gif =  in  

RESULTS BOX: 

2. A rectangle has a length of 12 centimeters and a width of 4 centimeters. Find the perimeter.
ANSWER BOX:  p_0.gif =  cm  

RESULTS BOX: 

3. Find the perimeter of a regular hexagon with each side measuring 8 meters.
ANSWER BOX:  p_0.gif =  m  

RESULTS BOX: 

4. The perimeter of a square is 20 feet. How long is each side?
ANSWER BOX:  s_0.gif =  ft  

RESULTS BOX: 

5. The perimeter of a regular pentagon is 100 centimeters. How long is each side?
ANSWER BOX:  s_0.gif =  cm  

RESULTS BOX: 

IXL