Question

A regular decegom has a perimeter of 150 in and an apothem of ≈ 23.1 in. What is the area of this polygon to the nearest tenth of a square foot?

Answer 1

Given:

Given that the perimeter of a regular decagon is 150 inches.

The apothem of a regular decagon is 23.1 inches.

We need to determine the area of the polygon.

Area of the regular decagon:

The area of the regular decagon can be determined using the formula,

$A=\frac{1}{2}ap$

where a is the apothem and p is the perimeter of the polygon.

Substituting the values, we get;

$A=\frac{1}{2}(23.1 \times 150)$

Multiplying, we get;

$A=\frac{1}{2}(3465)$

Dividing, we get;

$A=1732.5 \ in^2$

Thus, the area of the regular decagon is 1732.5 square inches.