Question

The similarity ratio of two similar polygons is 2:3. Compare
the smaller polygon to the larger polygon. Find the ratio
of their areas.

Answer 1

Answer:

The ratio of their areas is 4:9

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ---> the scale factor

x ---> the area of the smaller polygon

y ---> the area of the larger polygon

$z^2=\frac{x}{y}$

we have

$z=\frac{2}{3}$ ---> the scale factor is given

substitute

$(\frac{2}{3})^2=\frac{x}{y}$

$\frac{4}{9}=\frac{x}{y}$

Rewrite

$\frac{x}{y}=\frac{4}{9}$

therefore

The ratio of their areas is 4:9