Question

10. The perimeter of a regular nonagon is 162 inches. The apothem is 97.8 inches. Find the area.

Answer 1

Answer:

The area of the regular nonagon is 7921.8 square inches.

Step-by-step explanation:

Geometrically speaking, the area of a regular polygon is determined by following area formula:

$A = \frac{p\cdot a}{2}$ (1)

Where:

$A$ - Area of the regular polygon, in square inches.

$p$ - Perimeter, in inches.

$a$ - Apothem, in inches.

If we know that $p = 162\,in$ and $a = 97.8\,in$, then the area of the regular nonagon is:

$A = 7921.8\,in^{2}$

The area of the regular nonagon is 7921.8 square inches.