How to Convert Perimeter Length to Area

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The perimeter of a shape is the total distance around it, while area describes the amount of surface the shape uses or covers. Perimeter and area calculation methods differ for every kind of shape. For instance, while you can find the area of a rectangle simply by multiplying its length by its width, a circle requires a more complex calculation. Learn to convert the most basic shapes' perimeters to areas and you can later progress to compound shapes.

Square Perimeters

Divide the perimeter by 4 to obtain the length of each side, since all four sides of a square are equal. For example, a square with a perimeter of 36 inches would have sides that measure 9 inches each because

36 ÷ 4 = 9

Square the length of one side. For a square with 9-inch sides, work out

9 × 9 = 81

Add the proper unit of measure to the area. A square with a perimeter of 36 inches has an area of 81 square inches.

Rectangle Perimeters

Determine the length of both the base and the height. These are the sides that are not parallel to one another. For example, say you have a rectangle with a base of 6 cm and a height of 7 cm.

Multiply the base by the height. Work out

6 × 7 = 42

Add the proper unit of measure. In this example, the area of the rectangle is 42 cm square.

Triangle Perimeters

Determine the length of the base of the triangle. For example, say you have a triangle with a base of 3 feet.

Calculate the height of the triangle. Say you have a triangle with a height of 12 feet.

Multiply the length of the base by the length of the height. Work out

3 × 12 = 36

Divide by 2. Work out

36 ÷ 2 = 18

Add the proper unit of measure. The area of the triangle is 18 square feet.

Circle Circumference

Divide the circle's perimeter, also known as the circumference, by pi (3.14159265) to get the diameter of the circle. For example, say you have a circle with a circumference of 40 inches. Work out

40 ÷ 3.14159265 = 12.732

Divide the diameter by 2 to give you the length of the radius. Work out

12.732 ÷ 2 = 6.366

Multiply the radius by itself. In this example, work out

6.366 × 6.366 = 40.526

Multiply by pi (3.14159265). Work out

40.526 × 3.14159265 = 127.316

Add the proper unit of measure. The area of the circle is 127.316 square inches.