Question

These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given. Find its area and round to the nearest tenth.

Answer 1

`36.5\ cm^(2)`

Explanation:

step 1

Find the scale factor

we know that

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

Let

z ----> the scale factor

x----> the perimeter of the larger figure

y ----> the perimeter of the smaller figure

`z=(x)/(y)`

we have

`x=28\ cm`

`y=20\ cm`

substitute

`z=(28)/(20)=1.4`

step 2

Find the area of the larger figure

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 larger figure

y ----> the area of the smaller figure

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

we have

`z=1.4`

`y=18.6\ cm^(2)`

substitute

`1.4^(2) =(x)/(18.6)`

`x=1.96*(18.6)=36.5\ cm^(2)`