Question

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

Answer 1

The area of the regular nonagon is 7921.8 square inches.

Explanation:

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

`A = (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.