SOLUTION: Regular octagon ABCDEFGH has a side length of 2cm. Find the area of square ACEG

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Question 1179702: Regular octagon ABCDEFGH has a side length of
2cm. Find the area of square ACEG
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let the side of square be a
the area A=a%5E2

since <+ABC (interior angle of the octagon) is 135°, we can use cosine formula to calculate a

a%5E2=2%5E2%2B2%5E2-2%2A2%2A2%2Acos%28135%29

a%5E2=8-8%2Acos%28135%29....write cos%28135%29 as a cos%28180-45%29=cos%28-45%29=-cos%2845%29

a%5E2=8-8%2A%28-cos%2845%29%29............-cos%2845%29=-sqrt%282%29%2F2

a%5E2=8-8%2A%28-sqrt%282%29%2F2%29

a%5E2=8%2B4sqrt%282%29

a%5E2=13.7

=> the area A=13.7cm%5E2