SOLUTION: One square is placed upon each other so that a regular octagon is formed, along with eight right isosceles triangles each with its hypotenuse on a side of the octagon. If the perim
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Question 1101865: One square is placed upon each other so that a regular octagon is formed, along with eight right isosceles triangles each with its hypotenuse on a side of the octagon. If the perimeter of the octagon is 12 cm, find the perimeter of the star, in cm.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The perimeter of the octagon is 12, so the length of each side is 12/8 = 3/2.
In each isosceles triangle, the base is sqrt(2) times the length of each leg. Since the base has length 3/2, each leg has length (3/2) divided by sqrt(2), or 3*sqrt(2)/4.
The perimeter of the star consists of 16 of those legs; the perimeter of the star is 16*(3*sqrt(2)/4) = 12*sqrt(2).
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