Key Concepts: Areas of Similar Figures

Area Ratio Theorem

If two similar figures have a scale factor of a : b, then the ratio of their areas is a² : b².

Example

If two similar triangles have sides in ratio 3 : 5, their areas are in ratio 9 : 25.

Key Skills

• Find the ratio of areas given the scale factor.
• Find the scale factor given the ratio of areas (take the square root).
• Use area ratios to find unknown areas of similar figures.