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# polygons

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An octagon is inscribed in a square so that the vertices of the octagon trisect the sides of the square. The perimeter of the square is 108 centimeters  What is the perimeter of the octagon?

Apr 20, 2021

$\dfrac{104}{3\cdot4}=9$ which is the length of one of the octogon's side lengths, and the diagonals are 45-45-90 triangles, so the other side of the octogon is $3\sqrt2$. so, $(3+3\sqrt2)\cdot4=\boxed{12+12\sqrt8}$