Question

A regular heptagon has sides measuring 3.2 inches and an apothem that measures 2.9 inches. What is the area of this heptagon?

Answer 1

32.48 square inches

Explanation:

The area of a polygon is
`A=(nsa)/(2)` where
`n` is the number of sides of the polygon,
`s` is the side length of the polygon, and
`a` is the length of the apothem.

We are given the polygon is a heptagon, so it has 7 sides, making
`n=7`

We are given the heptagon's side length is 3.2 inches, making
`s=3.2`

We are also given an apothem of 2.9 inches, making
`a=2.9`

Therefore, by using the formula for the area of a polygon, we get
`A=(nsa)/(2)=(7*3.2*2.9)/(2)=(64.96)/(2)=32.48`

In conclusion, the area of the heptagon is 32.48 square inches