Area, Perimeter & Volume

Measuring shapes is a core part of the GL 11+ Mathematics exam. You need to know how to calculate the perimeter (distance around), area (space inside), and volume (space inside a 3D shape). This lesson gives you the formulas and methods for every shape you might encounter.

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Perimeter

Perimeter is the total distance around the outside of a 2D shape. It is measured in units of length (cm, m, km).

How to Find the Perimeter

Add up the lengths of all the sides.

Worked Example: A rectangle is 8 cm long and 5 cm wide. Find its perimeter.

• Perimeter = 8 + 5 + 8 + 5 = 26 cm
• Or use the formula: Perimeter = 2 × (length + width) = 2 × (8 + 5) = 2 × 13 = 26 cm

Perimeters of Compound Shapes

For irregular shapes, find any missing side lengths first, then add all sides.

Worked Example:

    6 cm
   ________
  |        |
  |        | 3 cm
  |   _____|
  |  | 2 cm
  |  |
  |__|
   4 cm