The perimeter of a shape is the distance around its edge. For a pentagon -- a shape with five straight sides -- the perimeter is equal to the sum of the lengths of a pentagon's five sides. The formula to find a pentagon's perimeter depends on whether that pentagon is a regular pentagon or an irregular pentagon.
The Perimeter of a Regular Pentagon
A regular pentagon is a pentagon that has five sides of equal length. Because each side is of equal length, you can find the perimeter of a regular pentagon by multiplying the length of one side by five.
So, let P represent the perimeter and s represent the side.
P = 5 x s
The Pentagon building in Arlington, Virginia is an excellent example of a regular pentagon. Each of the Pentagon's five sides are 921 feet long. You calculate the perimeter of the Pentagon by multiplying 921 feet by 5:
P = 5 x 921 feet
P = 4605 feet
So, the Pentagon has a perimeter of 4,605 feet.
The Perimeter of an Irregular Pentagon
An irregular pentagon has five straight sides, but the sides aren't all equal. Since the perimeter of any shape is equal to the sum of the lengths of all of that shape's sides, to find the perimeter of an irregular pentagon, you add all five sides individually:
P = s1 + s2 + s3 + s4 + s5
For example, the home plate in a baseball diamond is an example of an irregular pentagon. Home plate has one 17-inch side, two 12-inch sides and two 8.5-inch sides. To find the perimeter, add these lengths together:
P = 17 inches + 12 inches + 12 inches + 8.5 inches + 8.5 inches
P = 58 inches
So, home plate has a perimeter of 58 inches.
To find the perimeter of other irregular polygons, you apply the same basic formula: you add the length of each side individually.
- Photo Credit Sylvie Bouchard/iStock/Getty Images
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