Question

Find the area of a regular polygon that has 15 sides and a perimeter 120ft.

Please answer fast

Answer 1

Let 's' be the length of a side of the polygon.

Then,

perimeter = 15s

or, 120 = 15s

or, s = 8ft.

The area of regular polygon having 'n' number of sides with each of length 's' is given by:

A =
`[{(s)/(2tan((180)/(n)) )} (n)(s)]^(2)`

According to question,

s=8ft, n = 15

Therefore, Area =
`[(8)/(2tan((180)/(15)) )(15)(8)] = [(480)/(2tan(12))] = (240cot12)` ≈1129.11sq. ft