Question

Two 7-sided polygons are similar. A side of the larger polygon is 6 times as long as the corresponding side of the smaller polygon. What is the ratio of the area of the larger polygon to the area of the smaller polygon?

Answer 1

7-side polygon is heptagon or septagon.
Go to wikipedia and type
"heptagon"
On en.wikipedia you have all about heptagon.

Area is:

A=3.633912444*a^2
a is side lenght

Area of smaller heptagon is:

A1=3.633912444*(a1)^2
a1 lenght side of smaller polygon

Larger side lenght is:
a2=6*a1
a2 lenght side of larger polygon

A2=3.633912444*(a2)^2
=3.633912444*(6*a1)^2
=3.633912444*36*(a1)^2

(A2/A1)=36