SOLUTION: It has been done before on this website but the question was wrong:
Two identical squares with side of (1+sqrt(2))m overlap to form a regular octagon. What is the area of the oc
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Question 1209920: It has been done before on this website but the question was wrong:
Two identical squares with side of (1+sqrt(2))m overlap to form a regular octagon. What is the area of the octagon?
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!
When the two squares overlap to form a regular octagon, the regions inside the squares and outside the octagon are eight isosceles right triangles.
Let x be the side length of each of those triangles; then x*sqrt(2) is the length of the hypotenuse, which is the side length of the octagon.
The side length of each square is then 2x+x*sqrt(2). Since the side length of the square is 1+sqrt(2),
The side length of the octagon, x*sqrt(2), is then
The area of a regular octagon with side length s is
The side length of our octagon is 1, so the area is
ANSWER:
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