Mathematics (Core)Exam code: 0580

Area and Perimeter

Lengths, Areas and Volumes

PractiseFlashcards

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 dropped from the inner corner to the base, showing that the 17 cm base is the 3 cm top plus the 14 cm edge
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
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 horizontal ledge of the step is 3 cm because the 18 cm and 15 cm sides differ by that much
Source: Perimeter by Save My Exams
  • Pythagoras supplies a sloping side where a right angle is 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 four of its corners, 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

Build on this topic

Check your understanding11 exam questions, marked instantlyTest your recall12 flashcards on the key facts