Question

A new business center in town was built in a shape of a regular nonagon. Each side is 160 feet long which is the area occupied by the business center

Answer 1

Answer:

158,254.08 ft²

Step-by-step explanation:

A nonagon is a polygon with 9 sides and 9 angles.  A regular nonagon has all equal sides and all equal angles.  In order to find the area of a nonagon, you can use the formula:

A = $\frac{9}{4}a^{2}cot(\frac{180}{9})$ where 'a' represents the length of one side

Calculating the known measurements ahead of time, we get a condensed, or simplified formula:

A = 6.1818 x a²

Using the side length of 160 ft:

A = 6.1818 x 160² = 158,254.08 ft²