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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.
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![[IMAGE]](images/fence_perimeter.gif)
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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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Example 1:
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Find the perimeter of a
triangle
with sides measuring 5 centimeters, 9 centimeters and 11 centimeters.
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![[IMAGE]](images/scalene_triangle.gif)
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Solution:
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P = 5 cm + 9 cm + 11 cm = 25 cm
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Example 2:
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A
rectangle
has a length of 8 centimeters and a width of 3 centimeters. Find the perimeter.
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![[IMAGE]](images/rectangle_8x3.gif)
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Solution 1:
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P = 8 cm + 8cm + 3 cm + 3 cm = 22 cm
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Solution 2:
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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.
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In the next few examples, we will find the perimeter of other polygons.
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Example 3:
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Find the perimeter of a
square
with each side measuring 2 inches.
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![[IMAGE]](images/square_2X2.gif)
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Solution:
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= 2 in + 2 in + 2 in + 2 in = 8 in
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Example 4:
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Find the perimeter of an
equilateral triangle
with each side measuring 4 centimeters.
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![[IMAGE]](images/equilateral_triangle.gif)
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Solution:
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= 4 cm + 4 cm + 4 cm = 12 cm
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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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Example 3:
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Find the perimeter of a square with each side measuring 2 inches.
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Solution:
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This regular polygon has 4 sides, each with a length of 2 inches. Thus we get:
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= 4(2 in) = 8 in
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Example 4:
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Find the perimeter of an equilateral triangle with each side measuring 4 centimeters.
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Solution:
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This regular polygon has 3 sides, each with a length of 4 centimeters. Thus we get:
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= 3(4 cm) = 12 cm
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Example 5:
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Find the perimeter of a regular pentagon with each side measuring 3 inches.
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![[IMAGE]](images/pentagon.gif)
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Solution:
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= 5(3 in) = 15 in
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Example 6:
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The perimeter of a regular hexagon
is 18 centimeters. How long is one side?
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![[IMAGE]](images/regular_hexagon.gif)
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Solution:
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= 18 cm
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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 ().
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= 18 cm ÷ 6
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= 3 cm
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Summary:
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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.
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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.
