Answer:
[tex]36.5\ 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 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
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=28\ cm[/tex]
[tex]y=20\ cm[/tex]
substitute
[tex]z=\frac{28}{20}=1.4[/tex]
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
[tex]z^{2} =\frac{x}{y}[/tex]
we have
[tex]z=1.4[/tex]
[tex]y=18.6\ cm^{2}[/tex]
substitute
[tex]1.4^{2} =\frac{x}{18.6}[/tex]
[tex]x=1.96*(18.6)=36.5\ cm^{2}[/tex]
