What Is Perimeter?

The term "perimeter" refers to the distance all the way around the outside edge of a shape. It's also one of the easiest ways to measure a shape in the real world. You can measure the perimeter of a square on paper with a ruler, walk around the perimeter of a building or fenced yard, or even measure the perimeter of a circle (which is also called the circumference) with a piece of string. Depending on the shape, you can sometimes use what you know about the perimeter to find out other information about the shape's dimensions.

If your shape is round, its perimeter has a special name – the circumference. The easiest way to measure circumference on paper is with a piece of string, which you then hold against a ruler to read the measurement. When you encounter a round perimeter in the real world – for example, measuring the perimeter of a hole in the ground – you might walk around it, using a GPS or an old-fashioned measuring wheel to mark the distance.

For triangles and even irregular shapes made up straight lines joined by angles, you must measure each individual side, and then add them together to compute the perimeter. So if you have a triangle with three sides that measure 5 inches, 4 inches and 2 inches, its perimeter is:

\(5 \text{ inches} + 4 \text{ inches} + 2 \text{ inches} = 11 \text{ inches}\)

For squares and rectangles, you can simplify things a bit. Because all four sides of a square are equal, a square's perimeter is 4​a​ where ​a​ is the length of any of its sides. So if one side of the square measures 4 inches, they all measure 4 inches, and its perimeter is:

\(4 \text{ inches} + 4 \text{ inches} + 4 \text{ inches} + 4 \text{ inches} = 4 \text{ inches} × 4 = 16 \text{ inches}\)

On a rectangle, each set of opposite sides is equal to its mate. So if you can measure the length of any two ​adjoining​ sides, the perimeter of the rectangle is twice that. If you have a rectangle where one side measures 5 inches and the adjoining side measures 3 inches, that would give you:

\(2 × (5 \text{ inches} + 3 \text{ inches}) = 2 × (8 \text{ inches}) = 16 \text{ inches}\)

as the rectangle's perimeter.

If you know the circumference of a circle, you can use that information to calculate the area of the circle using the formula

\(A = \frac{C^2}{4π}\)

where A is the area of the circle and C is its circumference. If your circle has a circumference of 25 feet, you'd substitute 25 into the formula and then solve for A as follows.

1. Substitute the Circumference Into the Formula

\(A = \frac{(25 \text{ ft})^2}{4π}\)

2. Simplify the Fraction

\(A = \frac{625 \text{ ft}^2}{12.56}\)

3. Work the Division in the Fraction

\(A = 49.76 \text{ ft}^2\)

So the area of a circle with the perimeter or circumference of 25 feet is 49.76 ft².

Calculating the area of a square based on its perimeter is much easier:

1. Divide the Perimeter by 4

Divide the square's perimeter by 4; this gives you the length of one side. So if the square had a perimeter of 36 inches, you have:

\(\frac{36 \text{ inches}}{4} = 9 \text{ inches}\)

for the length of one side.

2. Square the Result

Squaring the result of Step 1 will give you the area of the square. To continue the example:

\((9 \text{ in})^2 = 81 \text{ in}^2\)

So the area of a square with a perimeter of 36 inches is 81 in².