![[IMAGE]](http://www.mathgoodies.com/lessons/vol1/images/fence_perimeter.gif)
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. 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.
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![[IMAGE]](http://www.mathgoodies.com/lessons/vol1/images/scalene_triangle.gif)
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.
![[IMAGE]](http://www.mathgoodies.com/lessons/vol1/images/rectangle_8x3.gif){kind=small}
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
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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.
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![[IMAGE]](http://www.mathgoodies.com/lessons/vol1/images/square_2X2.gif){kind=small}
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
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![[IMAGE]](http://www.mathgoodies.com/lessons/vol1/images/equilateral_triangle.gif){kind=small}
Example 4: Find the perimeter of an equilateral triangle with each side measuring 4 centimeters. Solution: = 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.
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Solution: This regular polygon has 4 sides, each with a length of 2 inches. Thus we get:
= 4(2 in) = 8 in
________________________________________Example 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:
= 3(4 cm) = 12 cm
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![[IMAGE]](http://www.mathgoodies.com/lessons/vol1/images/pentagon.gif)
Example 5: Find the perimeter of a regular pentagon with each side measuring 3 inches. Solution: = 5(3 in) = 15 in
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Example 6: The perimeter of a regular hexagon is 18 centimeters. How long is one side? Solution: = 18 cm
![[IMAGE]](http://www.mathgoodies.com/lessons/vol1/images/regular_hexagon.gif)
Let 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 ( ). = 18 cm ÷ 6
= 3 cm
Lesson derived from http://www.mathgoodies.com/lessons/vol1/perimeter.html
