Question 1101865
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The perimeter of the octagon is 12, so the length of each side is 12/8 = 3/2.<br>
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.<br>
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).