Question

the perimeter of pentagon A is 15 in. Its area is 30 in^2. The perimeter of pentagon B is 25 in. What is the area of pentagon B assuming that these pentagons are similar

Answer 1

Answer:

The area of pentagon B is $83\frac{1}{3}\ in^{2}$

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

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

substitute the values

$z=\frac{25}{15}$

Simplify

$z=\frac{5}{3}$ ----> 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

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

we have

$z=\frac{5}{3}$

$y=30\ in^{2}$

substitute and solve for x

$(\frac{5}{3})^{2}=\frac{x}{30}$

$(\frac{25}{9})=\frac{x}{30}$

$x=30*(\frac{25}{9})=83.33\ in^{2}$

convert to mixed number

$83.33=83\frac{1}{3}\ in^{2}$