The central angle of a regular polygon is 18 degrees. Th e perimeter of the polygon is 144 ft. What is the area of the polygon to the nearest tenth?

Given that the central angle of a polygon is 18, then the number of sides of the polygon will be:

360/18

=20 sides

thus the side length will be:

144/20

=7.2 ft

hence the area will b given by:

p=s*n

a=s/[2tan (180) / n]

where:

Area = (a*p) / 2

p=perimeter, s=side length, n=number of sides

p=7.2*20=144

a=7.2/[2tan (180/20) ]=22.73

thus

A = (144*22.73) / 2

A=1632.524 ft²