using 100 ft of fence material and building a regular octagon garden, what is the area of the garden?
8 sides, so each side = 12.5 ft
split the octogon into 8 isosceles triangles.
Consider one triangle, the central angle is 360/8 = 45°, so each base angle = 67.5°
tan 67.5 = height/6.25
height = 6.25(tan67.5) = 15.0888...
area of one triangle = (1/2)(12.5)(15.0888..)
= 94.3052..
area of whole thing =8(94.3052..) = 754.4417
check my arithmetic, I had my calculator keep all the digits as I went along