Question

A regular polygon has side length 10.9 in. The perimeter of the polygon is 87.2 in cm and the area is 392.4 in2. A second regular polygon has corresponding side lengths equal to 21.8 in. Find the area of the second polygon. Round to the nearest hundredth.
A. 98.1 in2
B. 1569.6 in2
C. 784.8 in2
D. 196.2 in2

Answer 1

Assuming that the two regular polygons have the same number of sides, then they are similar polygons.

Theorem:
If two polygons are similar, the square of the scale factor of the two polygons is equal to the ratio of any two corresponding area measurements of the polygons.

Answer 2

So,

the square of (10.9/21.8) = 392.4/x where x is the area of the second polygon

Answer 3

(10.9/21.8)^2 = 392.4/x

Answer 4

Now, we have to solve for x.

Answer 5

x=98.1

Answer 6

I got this: B. 1569.6 in2

Answer 7

(10.9/21.8)^2 = 392.4/x

.25 = 392.4/x

.25 x = 392.4

x = 1569.6

Answer 8

i think i get it now

Answer 9

@Ambbiiee That is what I was going to ask. Okay.