Answer:
The best estimate of the area of the larger figure is [tex]693\ cm^{2}[/tex]
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
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=12\ cm[/tex]
[tex]y=9\ cm[/tex]
substitute
[tex]z=\frac{12}{9}=\frac{4}{3}[/tex] -----> 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
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{4}{3}[/tex]
[tex]y=390\ cm^{2}[/tex]
substitute and solve for x
[tex](\frac{4}{3})^{2}=\frac{x}{390}[/tex]
[tex](\frac{16}{9})=\frac{x}{390}[/tex]
[tex]x=390*16/9=693.33\ cm^{2}[/tex]
