Answer:
The area of pentagon B is [tex]83\frac{1}{3}\ in^{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----> perimeter pentagon B
y----> perimeter pentagon A
[tex]z=\frac{x}{y}[/tex]
substitute the values
[tex]z=\frac{25}{15}[/tex]
Simplify
[tex]z=\frac{5}{3}[/tex] ----> scale factor
step 2
Find the area of pentagon B
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----> area pentagon B
y----> area pentagon A
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{5}{3}[/tex]
[tex]y=30\ in^{2}[/tex]
substitute and solve for x
[tex](\frac{5}{3})^{2}=\frac{x}{30}[/tex]
[tex](\frac{25}{9})=\frac{x}{30}[/tex]
[tex]x=30*(\frac{25}{9})=83.33\ in^{2}[/tex]
convert to mixed number
[tex]83.33=83\frac{1}{3}\ in^{2}[/tex]
