Question

Find the number of sides for a regular polygon if the area is 480, the side length is 10 and the apothem is 6.
Answer 30
16
8
4

Answer 1

Area= (1/2)ap
a=apothem
p=perimeter
We have:
Area=480
a=6
we need to find p:
\[480=(\frac{1}{2})(6)p \rightarrow \frac{480*2}{6}=p \rightarrow p=160\]
since it is a regular polygon, all the sides have equal length, so
160=10x
x=16
Thus the polygon has 16 sides