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

The ratio of their areas is 4:9

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=(x)/(y)`

we have

`z=(2)/(3)` ---> the scale factor is given

substitute

`((2)/(3))^2=(x)/(y)`

`(4)/(9)=(x)/(y)`

Rewrite

`(x)/(y)=(4)/(9)`

therefore

The ratio of their areas is 4:9