SOLUTION: how do you find the area of an octagon with a radius of 10??

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Question 289972: how do you find the area of an octagon with a radius of 10??
Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
how do you find the area of an octagon with a radius of 10?
A area = 1/2 * n * r^2 * sin((2pi)/n)
this is the area of 8 triangles arranged in a circle
area of 1 triangle = 1/2 * r^2 * sin(2pi/8)
area of 1 triangle = 1/2 * r^2 * sin(pi/4)
(r^2 = 100)
(sin pi/4 = sin (45 deg.))
area of 1 triangle = 1/2 * r^2 * sqrt(2)/2) = sqrt(2)/4 * 100
area of 1 triangle = 25sqrt(2)
total area = 8 * 25 * sqrt(2)= 200sqrt(2)