Ratio of areas of similar triangles

For two similar triangles $ABC$ and $DEF$, if the ratio of corresponding sides is $AB:DE = k:1$, then the ratio of their areas is $k^2:1$. In general, $\frac{\text{Area of } \triangle ABC}{\text{Area of } \triangle DEF} = \left(\frac{AB}{DE}\right)^2$

Important properties

• The ratio of areas of similar triangles equals the square of the ratio of any pair of corresponding sides.

• This property holds for all pairs of similar triangles, regardless of orientation or position.

• If the ratio of perimeters is $k:1$, the ratio of areas is $k^2:1$.