How Do I Calculate the Perimeter of a Rectangle?

You can find the perimeter of a rectangle by summing the four sides' lengths.

A perimeter is the length of the boundary of a flat shape. Put another way, it is it the length all around the edge of the shape. For example, the perimeter of a circle is the same as its circumference. You can measure the perimeter of a rectangle easily if you know its length and its width. If you are given its area and the length of one of its sides, you can still calculate the perimeter but it takes more steps.

Instructions

1. Calculate the perimeter of a rectangle by adding up the length of its sides. For example, if a rectangle has two opposite sides that are 3 feet long each, and the other two sides are both 2 feet long each, then 3 + 3 + 2 + 2 = 10 feet is the length all around the edge of the rectangle, or, the perimeter.

2. Calculate the perimeter of the rectangle from the area and the length of one of the sides by using the area formula. The area of a rectangle is length times width.

   For example, the 3 foot by 2 foot rectangle above has an area of 6 square feet. Suppose you know that a different rectangle has area 10 feet squared and two sides out of four that are 2 feet long. Then 10 feet = area = side 1 x side 2 = 2 feet x side 2. So side 2 must be 5 feet long. So the length and width must be 5 feet and 2 feet. So the perimeter is 5 + 5 + 2 + 2 = 14 feet long.

3. Calculate the perimeter of a rectangle from the area and a relation between the sides by finding representing one of the sides with a variable and then solving for it.

   For example, if you know that a new rectangle, different from the rectangles mentioned above, has an area of 12 square feet and the length is one-third longer than the width, then set up two equations relating the length, L, and width, W, and solve for each variable, one at a time. Continuing with the example, area = 12 = L x W. You also know that L = (4/3) W, because L is one-third longer than W. Plug this L into the other equation so area can be written in terms of W only. 12 = L x W = (4/3) W x W = 4/3 W^2. Here, "^2" means W is squared. So 12 = 4/3 W^2. Multiply by sides of the equation by ¾ to get 9 = W^2. So W must be 3. Since L = (4/3) W, then L must be 4. So the perimeter is L + L + W + W = 4 + 4 + 3 + 3 = 14 feet long. This is the rectangle's perimeter.

References

• SparkNotes: Perimeter of a Rectangle
• Birmingham Grid for Learning: Perimeter and Area