Question

Brennan is making a poster for the drama club’s new production. It is a regular pentagon with side lengths of 12 inches. The school wants to put up a giant replica of the poster during athletic events.

If the length of each side is 8 times the original, how many times larger is the area of the replica than the area of the original?

Answer 1

Do you know the formula to figure out the area of a regular pentagon?

Answer 2

no i dont think so

Answer 3

is it 1.72*x^2

Answer 4

The formula for calculating the area of a regular polygon is
\[A=\frac 12 nsr \text{ where } n= \text{ the number of sides, } s= \text{length of side, and }r=\text{ apothem}\]

Answer 5

how do i figure out the problem though ?

Answer 6

Well, you don't actually need to know what the area is, you only want to know how much bigger the bigger pentagon than the small one. The number of sides of both pentagons remain the same but the length of the sides of the bigger pentagon is 12 times bigger than the smaller and therefor, the apothem is 12 times larger as well. So if the area of the smaller pentagon is given by \[A _{s}=\frac 12 nsr\]The area of the bigger is given by\[A _{l}=\frac 12 n(12s)(12r)=144 (\frac 12 nsr)=144 A _{s}\]

Answer 7

im confused?