use trigonometry to find the area of a

Question

use trigonometry to find the area of a regular 20- gon with each side = 6 in

1. (please help !!!) i need answers asap bc i am stuck finding the Apothem and perimeter... i js need answers bc i am very stuck and confused :///

Answer 1

there's a formula for the area of a regular polygon of sides = n, length of side =s

A= s^2n/4tan(180/n)

for n=20, s=6

A= 36(20)/4tan6 = 180/tan6 = about 1712.7 square inches

for example a square of side=1 would have area = (1)^2(4)/4tan(180/4) = 1/tan45 = 1/1 = 1 square inch