Question

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?

Answer 1

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