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



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.


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


Example 5:

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


Solution:

= 5(3 in) = 15 in


Example 6:

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


Solution:

= 18 cm


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



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: .
To find the perimeter of a regular polygon, multiply the number of sides by the length of one side.
