Ratios of areas of similar figures

For any two similar plane figures, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

Important properties

• If two figures are similar with side lengths in ratio $k:1$, then their areas are in ratio $k^2:1$.

• This rule applies to all similar polygons and circles.

• The ratio of perimeters of similar figures is equal to the ratio of their sides, not squared.