Question

What is the area of a regular polygon with 16 sides and side length 4 inches? PLease explain in detail with a diagram. Thank You.

Answer 1

Area is 321.6 square inches.

Explanation:

A regular polygon with 16 sides is a Regular Hexadecagon. Regular means all sides are equal dimension. See image attached.

Side length is 4 inches.

side length=s=4 inches

1. You need to calculate the apothem.

Apothem=s*2.51367

Apothem=10.054

2. You can use the formula to calculate de area of an hexadecagon:

`A=(Perimeter*Apothem)/(2)`

Perimeter=16 sides*4inches

Perimeter= 64 inches

`A=(64*10.054)/(2)`

`A=321.6 inches^(2)`