How do I find the edge length?

Question

Kaitlin can't remember the formula for the area of a circle. She decides to approximate the area of a circle by circumscribing a regular 18 -gon around the circle. If her approximation of the area is 408 , what is the edge length of the 18 -gon?

Answer 1

If you derive the formula for the area of an n-gon given s, the length of a side, you get the following:

A=(n)(s²)/4tanθ where n=18 and θ=180/18=10

408=(18)(s²)/4tan10º

408=(18)(s²)/4(0.17632698)

408=(18)(s²)/0.7053076

408*0.7053076=18s²

287.7655=18s²

s²=287.7655/18

s²⁼15.9869

s=√15.9869

s=3.998

because you have an approximation, I would say that the edge length is 4