Question

are any two regular polygons similar. The area of the smaller figure is about 390 cm^2. choose the best estimate of the area of the larger figure

Answer 1

The best estimate of the area of the larger figure is
`693\ cm^(2)`

Explanation:

step 1

Find the scale factor

we know that

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

Let

z----> the scale factor

x-----> the corresponding side of the larger figure

y-----> the corresponding side of the smaller figure

so

`z=(x)/(y)`

we have

`x=12\ cm`

`y=9\ cm`

substitute

`z=(12)/(9)=(4)/(3)` -----> the scale factor

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

so

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

we have

`z=(4)/(3)`

`y=390\ cm^(2)`

substitute and solve for x

`((4)/(3))^(2)=(x)/(390)`

`((16)/(9))=(x)/(390)`

`x=390*16/9=693.33\ cm^(2)`