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

Answer:

32.48 square inches

Step-by-step explanation:

The area of a polygon is $A=\frac{nsa}{2}$ 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$A=\frac{nsa}{2}=\frac{7*3.2*2.9}{2}=\frac{64.96}{2}=32.48$

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