Math Core

Imagine you want to put a fence around a garden. How much fence do you need? You need to know the distance all the way around the garden. That distance is called the perimeter.

Walking around the edge

Picture an ant walking along the edge of a shape. It starts at one corner, walks along every side, and ends up back where it started. The total distance the ant walks is the perimeter.

Definition

Perimeter

The perimeter of a shape is the total distance around it. To find it, add the lengths of all the sides.

Perimeter is a length, so it uses length units: inches, feet, centimeters or meters.

Adding the sides

This rectangle is 6 centimeters long and 4 centimeters wide.

A rectangle 6 cm long and 4 cm wide.

A rectangle has 4 sides. Opposite sides are the same length, so the sides are 6, 4, 6 and 4 centimeters.

6 + 4 + 6 + 4 = 20

The perimeter is 20 centimeters.

Tip

Mark each side with your finger as you add it. That way you won't skip a side or count one twice.

Rectangles and squares

A rectangle often shows only two lengths, the length and the width. Don't forget the two sides that aren't labeled! They match the sides across from them.

A square has 4 sides that are all the same length. So you can add the side 4 times, or multiply it by 4.

Finding perimeter

Any shape: add all the side lengths.
Rectangle: length + width + length + width.
Square: side + side + side + side, which is the same as $4 \times \text{side}$ .

Worked example: A triangle

A triangle has sides that are 5 inches, 7 inches and 9 inches long. What is its perimeter?

Add all three sides: $5 + 7 + 9 = 21$ .

The perimeter is 21 inches.

Worked example: A square

A square tile has sides that are 6 centimeters long. What is its perimeter?

All 4 sides are 6 centimeters. $6 + 6 + 6 + 6 = 24$ , or $4 \times 6 = 24$ .

The perimeter is 24 centimeters.

Finding a missing side

Sometimes you know the perimeter but one side length is missing. Add the sides you know. Then ask: how much more do I need to reach the perimeter?

Worked example: A missing side

A shape has 4 sides. Three of them are 4 feet, 6 feet and 5 feet long. The perimeter is 20 feet. How long is the fourth side?

Add the sides you know: $4 + 6 + 5 = 15$ .

The whole trip around is 20 feet. Subtract: $20 - 15 = 5$ .

The fourth side is 5 feet long.

Worked example: A missing width

A rectangle has a perimeter of 18 meters. Its length is 5 meters. What is its width?

A rectangle has two lengths: $5 + 5 = 10$ meters.

The two widths make up the rest: $18 - 10 = 8$ meters.

The two widths are equal, so each one is $8 \div 2 = 4$ meters. The width is 4 meters.

Check: $5 + 4 + 5 + 4 = 18$ . ✓

Common mistake

When a rectangle shows only two numbers, don't just add those two. $6 + 4 = 10$ is only half of the way around. Add all 4 sides to get $20$ .

Practice

Practice 1

A triangle has sides that are 3 cm, 4 cm and 5 cm long. What is its perimeter, in centimeters?

Type a number.

Practice 2

A rectangle is 7 meters long and 2 meters wide. What is its perimeter, in meters?

Type a number.

Practice 3

A square has sides that are 9 inches long. What is its perimeter, in inches?

Type a number.

Practice 4

Which unit could you use to measure the perimeter of a notebook?

Practice 5

A shape has 5 sides. Each side is 4 feet long. What is its perimeter, in feet?

Type a number.

Practice 6

A shape has 4 sides. Three of the sides are 6 cm, 8 cm and 5 cm long. The perimeter is 25 cm. How long is the fourth side, in centimeters?

Type a number.

Practice 7

A rectangle has a perimeter of 30 cm. Its length is 9 cm. What is its width, in centimeters?

Type a number.

Practice 8

Rosa has 40 inches of ribbon. She glues ribbon all the way around a picture frame shaped like a rectangle. The frame is 10 inches long and 8 inches wide. How many inches of ribbon does she have left?

Type a number.