Perimeter

The perimeter of a shape is the distance all the way round it: add the lengths of all its sides. For a rectangle, perimeter = 2 × (length + width). Perimeter is a length, so it is measured in cm, m or km.

Key facts

  • Perimeter is the distance all the way round a shape: add up all its sides.
  • Rectangle: area = length × width; perimeter = 2 × (length + width).
  • A square has 4 equal sides, so its perimeter is 4 × the side.
  • Rectilinear shapes: work out any missing sides from the others first.
  • Shapes with the same area can have different perimeters.

Worked examples

Example 1

Find the perimeter of a rectangle 6 cm long and 4 cm wide.

  1. Add the lengths of all four sides. 6 + 4 + 6 + 4 = 20 cm

Answer: 20 cm

Example 2

A triangle has sides of 5 cm, 7 cm and 8 cm. What is its perimeter?

  1. Add the lengths of all three sides. 5 + 7 + 8 = 20 cm

Answer: 20 cm

Example 3

A square has sides of 9 cm. What is its perimeter?

  1. A square has 4 equal sides. 4 × 9 = 36 cm

Answer: 36 cm

Example 4

Find the perimeter of this L-shape. All corners are right angles; lengths are in cm.

  1. The short side across the top of the step: 10 − 5 = 5 cm
  2. The short side going up the step: 7 − 4 = 3 cm
  3. Add all six sides. 10 + 4 + 5 + 3 + 5 + 7 = 34 cm

Answer: 34 cm

Example 5

A rectangle has a perimeter of 30 cm. It is 9 cm long. How wide is it?

  1. The length and the width add up to half the perimeter. 30 ÷ 2 = 15 cm
  2. Take away the length. 15 − 9 = 6 cm

Answer: 6 cm

Example 6

A rectangle is 12 m long and 7 m wide. Use a formula to find its perimeter.

  1. Perimeter = 2 × (length + width). 2 × (12 + 7) = 38 m

Answer: 38 m

Example 7

Two rectangles both have an area of 24 cm². One is 6 cm by 4 cm; the other is 12 cm by 2 cm. Which has the longer perimeter?

  1. 6 cm by 4 cm: 2 × (6 + 4) = 20 cm
  2. 12 cm by 2 cm: 2 × (12 + 2) = 28 cm
  3. The same area can have different perimeters: the long, thin one has the longer perimeter.

Answer: 12 cm by 2 cm (28 cm, not 20 cm)