Answer:
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 = [tex][{\frac{s}{2tan(\frac{180}{n}) }} (n)(s)]^{2}[/tex]
According to question,
s=8ft, n = 15
Therefore, Area = [tex][\frac{8}{2tan(\frac{180}{15}) }(15)(8)] = [\frac{480}{2tan(12)}] = (240cot12)[/tex] ≈1129.11sq. ft
