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

Answer:

The best estimate of the area of the larger figure is $693\ cm^{2}$

Step-by-step 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

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

we have

$x=12\ cm$

$y=9\ cm$

substitute

$z=\frac{12}{9}=\frac{4}{3}$ -----> 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

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

we have

$z=\frac{4}{3}$

$y=390\ cm^{2}$

substitute and solve for x

$(\frac{4}{3})^{2}=\frac{x}{390}$

$(\frac{16}{9})=\frac{x}{390}$

$x=390*16/9=693.33\ cm^{2}$