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

The area of pentagon B is
`83(1)/(3)\ in^(2)`

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=(x)/(y)`

substitute the values

`z=(25)/(15)`

Simplify

`z=(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)=(x)/(y)`

we have

`z=(5)/(3)`

`y=30\ in^(2)`

substitute and solve for x

`((5)/(3))^(2)=(x)/(30)`

`((25)/(9))=(x)/(30)`

`x=30*((25)/(9))=83.33\ in^(2)`

convert to mixed number

`83.33=83(1)/(3)\ in^(2)`