Answer:
Area = 102
Step-by-step explanation:
Length 1 side of the octagon.
The formula for the side of an octagon (given the radius of 6) is
s^2 = 2*R^2(1 - cos(45) )
s^2 = 2*6^2(1 - sqrt(2)/2)
s^2 = 72 ( 1 - 0.707)
s^2 = 72*0.2929
s^2 = 21.09
s = sqrt(21.09)
s = 4.5922
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Height of one triangle =
H = R * cos(22.5)
H = 6 * 0.9329
H = 5.5433
===============
Area of 1 triangle
Area = 1/2 * s * h
Area = 1/2 * 4.5922*5.4433
Area = 12.7279
Area of 8 triangles
Area of 8 triangles = 1 triangle * 8
Area of 8 triangles = 101.82
Rounded that comes to 102
Comment
I'm sure you can find a formula for this on the internet, but it this is the way the formula works and if you break it down step by step, you can see how the formula works.
