Concept

Area Scale Factor

For similar figures, the ratio between their areas is called the area scale factor.

Area Scale Factor \frac{Area of Figure 2}{Area of Figure 1} or Area of Figure 2 : Area of Figure 1

The scale factor of the areas of similar figures can also be calculated by squaring the length scale factor of the figures.

Example Considering Similar Figures

Examine these two similar triangles.

It can be seen that the areas of

△ A B C

and

△ P Q R

are

3

and

27

square units, respectively. This is enough information to calculate the area scale factor.

Area Scale Factor = \frac{Area of Figure 2}{Area of Figure 1}

$Area of Figure 1 = 3$ , $Area of Figure 2 = 27$

Area Scale Factor = \frac{2 7}{3}

Calculate quotient

Area Scale Factor = 9