SOLUTION: What would the area of a octagon be if it the length of the sides are 4m

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Question 846939: What would the area of a octagon be if it the length of the sides are 4m
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Each central angle is %22360%B0%22%2F8=%2245%B0%22




The green line bisects the isosceles triangle,
so the angle at the top is 22.5° and the base
of the right triangle is 2m, so

tan(22.5°) = 2%2Fh

h*tan(22.5°) = 2

h = 2%2Ftan%28%2222.5%B0%22%29 = 4.828427125

So the area of the whole triangle is 

A = 1%2F2*b*h = 1%2F2*4*4.828427125 = 9.656854249

The area of the whole octagon is 8 times that or

9.656854249×8 = 77.254834

Incidentally h is called the "apothem".

Edwin