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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

Once you've worked out the answers, click "Next Step" to show the answer to each answer to each question!

1. Michelle’s garden is a rectangle. We know this because it talks about length and width (4-sided shapes have these) and we can conclude it is not a square, because the length and width are different, therefore all four sides are not equal.

2. The problem stated that Michelle’s garden is two feet longer than it is wide. We know Michelle’s garden is 4 feet wide, so we know that we have to add 2 to that number, resulting in 6. Thus, Michelle’s garden is 6 feet long.

3. In order to find the perimeter of Michelle’s garden, we have to add together all four sides. We know that two sides are 4 feet long, and the other two sides are 6 feet long. Therefore, we can solve the addition problem: 4 + 4 + 6 + 6 = 20 feet. Our answer is that the perimeter of her garden is 20 feet. This means that, when Michelle buys the material to build her fence, she’ll need 20 feet of material in order for the fence to be complete.

4.

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

Once you've worked out the answers, click "Next Step" to show the answer to each answer to each question!

1. We know that Andrew’s box is in the shape of a hexagon, and a hexagon has 6 sides. Therefore, Andrew’s box also has 6 sides.

2. All sides of Andrew’s box are the same length. We know this because the problem stated that we have a “regular” hexagon, and we know that regular means all sides are the same.

3. We can easily calculate the perimeter of Andrew’s lid to the box by using the following addition problem: 5 + 5 + 5 + 5 + 5 + 5 = 30 inches.