The perimeter of a polygon is the distance around the outside of the polygon. A polygon is 2dimensional; however, perimeter is 1dimensional and is measured in linear units. To help us make this distinction, look at our picture of a rectangular backyard. The yard is 2dimensional: it has a length and a width. The amount of fence needed to enclose the backyard (perimeter) is 1dimensional. 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 fencedin 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.  
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.  

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:
, where is the perimeter, is the length and 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.  
Solution:  = 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.  
Solution:  = 4 cm + 4 cm + 4 cm = 12 cm 
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