Perimeter

Perimeter simply measures the distance around an area. It can be measured in inches,
feet, yards, miles, centimeters, meters, kilometers, and so on (any standard distance
measurement). You can measure the perimeter of nearly any shape, you just add together
the measure of each of its sides. Much of the ability to figure out perimeter lies
in remembering the properties of certain shapes. We’ll go through several examples.

Perimeter of a Square

Taking the following square with side length 6 inches, calculate the perimeter.

In order to calculate perimeter, you need to add together the lengths of all four
sides of the square. You are given the length of one side. Remember, all sides of
a square are equal, so really you already have the measures of each side.

Then, you add them together, so 6 + 6 + 6 + 6 = 24 inches. Thus, 24 inches is your
final answer.

Perimeter of a Rectangle

Taking the following rectangle with length 8 inches and width 4 inches, calculate
the perimeter.

In order to calculate perimeter, you need to add together the lengths of all four
sides of the rectangle. You are given the length of one side and the width of one
side. Remember, opposite sides of a rectangle are equal, so really you already have
the measures of each side.

Then, you add them together, so 8 + 8 + 4 + 4 = 24 inches. Thus, 24 inches is your
final answer.

Perimeter of a Polygon

The perimeter of a polygon is calculated using the same method of adding together
each side. Remember that if all the sides are equal, you only need to know one side
of the polygon. If the sides are unequal, however, you do need to know the length
of each different side. Taking the following pentagon with side length 7, calculate
the perimeter.

A pentagon has five sides, and all of these sides are equal, therefore you can perform
the following calculation:

7 + 7 + 7 + 7 + 7 = 35

Perimeter Word Problems

Many times, perimeter problems will come to you in the form of word problems, so
that you’ll have to read them and then draw the picture and calculate the perimeter.
We’ll give you two examples of how to do this.

Example 1

Michelle was planting a garden. She wanted her garden to be fenced in, so she went
to the hardware store to buy fencing material. The salesperson asked Michelle how
big her garden would be. She thought about it, and then replied that her garden
would be 4 feet wide, and that it would be 2 feet longer (in length) than it is
wide. Answer the following questions:

1. What shape is Michelle’s garden?

2. How long is Michelle’s garden?

3. What is the perimeter of Michelle’s garden?

4. Draw and label Michelle’s garden.

Solution

Example 2

Andrew is going to build a box to hold his hats. He decides that each side should
be 5 inches long. He also decides to make this box in the shape of a regular hexagon.
Answer the following questions:

1. How many sides does Andrew’s box have?

2. Are all sides the same length? How do you know?

3. What is the perimeter of to Andrew’s box?

Solution