How do you find the Base area of a octagonal cyclinder?

Question

i have a geomertry test tomarrow and i forgot how to find it. please help

Answer 1

A regular octagon can be divided into 8 isosceles triangles with base L, the length of one side, and height W/2, where W is the width of the octagon across the flats. Using A = (1/2)bhfor each triangle and multiplying by 8, you get

At = (8)(1/2)(W/2)L = 2WL

There is a fixed relation between L and W for the octagon:

(L/2)//(W/2) = tan(45°/2)

L = Wtan(22.5°)

At = 2W^2tan(22.5°) ≈ 0.8284271W^2