0580

Area and Perimeter

Lengths, Areas and Volumes

Adding up the outside

  • The perimeter is the total distance round the edge of a shape, so it is a length and its units are mm, cm, m or km
  • Find it by adding every side, working round the shape once so nothing is counted twice or missed
  • For a regular shape it is the number of sides times the length of one, so a square of side x has perimeter 4x
  • A circle's perimeter has its own name, the circumference, and belongs to the circles topic

Missing lengths

  • Compound shapes usually leave some sides unlabelled, and they have to be worked out before adding
  • On an L-shape the two shorter horizontal sides together equal the long horizontal side opposite, and the same holds vertically
An L-shaped figure labelled 3 cm across the narrow top, 14 cm along the upper right edge and 17 cm along the base, with a dashed red line splitting it so the missing side can be found as 17 − 14 = 3 cm
Source: Perimeter by Save My Exams
  • Dashes on a diagram mark sides that are equal, and the question may state equalities in words instead
A compound shape shaped like an arrow with a step cut into its right-hand end, labelled 6 cm on one sloping side, 18 cm along the top, 2 cm and 4 cm down the step and 15 cm along the bottom, with two sloping sides marked equal by matching dashes
Source: Perimeter by Save My Exams
  • Pythagoras supplies a sloping side where a right angle is available
The same arrow-shaped figure with the two lengths that were missing filled in red: the second sloping side is 6 cm because it matches the first, and the step across the top is 3 cm because the 18 cm and 15 cm sides differ by that much
Source: Perimeter by Save My Exams
Exam tip

Write the perimeter as one long sum of every side, including the ones you worked out yourself. Mark schemes follow through from your own missing length, so a slip there still leaves the method mark available.

Worked example

Perimeter of an L-shaped room

The floor plan below shows a room. All the corners are right angles. Work out the perimeter of the room.

An L-shaped floor plan with right angles marked at each corner, labelled 3.2 m up the left side, 6 m along the bottom, 1.8 m up the right side and a 2.4 m step across the top; the top edge and the vertical part of the step are not labelled
Source: Problem-solving with areas by Save My Exams

Solution:

  • Two sides are unlabelled, so find those first
  • The two horizontal sides at the top must add to the 6 m base, so the top edge is 6 − 2.4 = 3.6 m
  • The two vertical sides on the right must add to the 3.2 m left side, so the step down is 3.2 − 1.8 = 1.4 m
  • Now add every side once, going round the shape
  • 3.6 + 1.4 + 2.4 + 1.8 + 6 + 3.2 = 18.4 m
  • Perimeter is a length, so the answer is in metres and not square metres