MathsYears 9–11Geometry - Properties of Shapes

Similar shapes and scale factors

Learn Similar shapes and scale factors for Years 9–11 pupils (ages 13–16). Free practice questions, lessons and worked examples — aligned to the UK National Curriculum.

What you'll learn

  1. 1

    Similar shapes have the same angles and their sides are all in the same ratio — the scale factor.

  2. 2

    To find the scale factor, divide a side on the larger shape by the matching side on the smaller.

  3. 3

    Two similar triangles have matching sides 4 cm and 12 cm. What is the scale factor?

  4. 4

    Area does NOT scale by the same factor. If lengths scale by k, areas scale by k² and volumes by k³.

  5. 5

    Two similar solids have lengths in ratio 1:3. Their areas are in ratio 1:9 and their volumes in ratio 1:27.

  6. 6

    Lengths scale by 2. What happens to the area?

  7. 7

    A shape is enlarged by scale factor 5. Its volume becomes how many times bigger?

Practise Similar shapes and scale factors with Whizlo

Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 13–16. Aligned to the UK National Curriculum.