Question

Two similar polygons have the scale factor 5:2. The area of the larger polygon is 100. Find the area of the smaller polygon?

Answer 1

The area of the smaller polygon is:

`(2/5)^2*100 = 4/25*100 = 16`

Explanation:

Area changes as the square of the change in length.

That is, if the lengths are double then the area is four times; if the lengths are halved, the area is one quarter, etc.

In our example, the lengths of the smaller polygon are `2/5` of the lengths of the larger one, so the area is `(2/5)^2 = 4/25` times the area of the larger one.

Answer 2

`area = 16`

Explanation:

Areas of similar figures are in the same ratio as the square of their sides.

We can write this as a proportion - the ratio of the sides is on the left, and the ratio of their areas on the right.

Note that because we are dealing with areas, the ratio of the sides is squared.

`(side_1)^2/(side_2)^2 = (area_1)/(area_2)`

`5^2/2^2 = 100/a" note:" (5/2)^2 = 5^2/2^2`

`a = (2^2xx100)/5^2`

`a = 16`