Thursday, November 22, 2012

Perimeter Part I

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.[IMAGE]
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.

Example 1:Find the perimeter of a triangle with sides measuring 5 centimeters, 9 centimeters and 11 centimeters.[IMAGE]
Solution:P = 5 cm + 9 cm + 11 cm = 25 cm

Example 2:rectangle has a length of 8 centimeters and a width of 3 centimeters. Find the perimeter.[IMAGE]
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:

P = 2L + 2W,  where P is the perimeter, L is the length and W 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.[IMAGE]
Solution:P = 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.[IMAGE]
Solution:P = 4 cm + 4 cm + 4 cm = 12 cm

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