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How to Find Perimeter from Area

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  • 0:04 How To Find Perimeter…
  • 0:27 Perimeter of a Square
  • 1:20 Perimeter of a Circle
  • 2:16 Perimeter of a Rectangle
  • 3:22 Formatting Answers
  • 4:38 Tips For All Regular Shapes
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Lesson Transcript
Instructor: Maria Airth

Maria has a Doctorate of Education and over 15 years of experience teaching psychology and math related courses at the university level.

Here, you'll learn the steps to find the perimeter of a square, circle or rectangle from the area of the given shape. You'll also read about the units of measurement used for area, and get tips for solving problems.

How To Find Perimeter From Area

Finding the perimeter a shape from its area depends on what shape you are using. To review, perimeter is the distance around the edge of a shape, while area is the space covered within the edges of a two-dimensional shape.

In this lesson, we'll learn how to find the perimeter of a square, circle or rectangle when given the shape's area.

Perimeter of a Square

Let's start with a square and learn by working through this sample problem. Find the perimeter of a square with an area of 64 square meters.

Step 1

Remember the formulas for both area and perimeter of a square. The area of a square is a = s 2, or side times side, while the perimeter is p = 4s, or 4 times s.

Step 2

Find the length of one side by plugging the area value into the formula and solving for s. In this case, 64=s2, so s=8.

Step 3

Substitute the value of s (the length of a side) into the perimeter formula and solve.

p =4 x 8, so p = 32

Perimeter of a Circle

Next, let's look at a sample problem to find the perimeter of a circle form its area. Find the perimeter of a circle with an area of 9pi.

Step 1

Remember the formulas for both area and perimeter of a circle. The area of a circle is a = pi * radius2, while the perimeter of a circle, more commonly known as the circumference, is p = 2pi * radius.

Step 2

Find the length the radius by substituting in the area and solving the formula

9p i= pi * r2

Divide by pi to get: 9 = r2

r=3

Step 3

Substitute the value of r into the perimeter formula

p = 2 * pi * 3

p = 6pi

Perimeter of a Rectangle

It's not possible to determine the perimeter of a rectangle given only the area. The area of a rectangle depends on two unknowns, the length and the width, so you must be given at least one side of the rectangle along with the area to determine the other side and, thus, the perimeter.

Let's look at a sample problem. Find the perimeter of a rectangle with length 4 and area 36m2.

Step 1

Remember the formula for perimeter and area of a rectangle. The area of a rectangle is a = length * width, while the perimeter is p = (2 * length) + (2 * width)

Step 2

Substitute the known values into the area formula

36 = 4 * w

36/4 = w

w=9

Step 3

Substitute values for length and width into the perimeter formula.

p = 2 * 4 + 2 * 9

p = 8 + 18 = 26

Formatting Answers

The answers for each of these calculations will be in standard units, not squared. You must use the same measurement that is used in the original problem to format your answer.

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