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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 number of square centimeters in the area of the octagon?

 Dec 4, 2018
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This will not be a regular octagon

The side of the square is 108/4  =  27

The side of the octagon along the side of the square = 27/3 = 9

And a octagon side adjacent to this one will form an isosceles right triangle with legs of 9

So...the area of one of these triangles is 9^2/2 = 81/2  cm^2

And there will be 4 of these ....one at each vertex of the square

So the total areas of these = 4*81/2 = 162 cm^2   (1)

And the area of the square is 27^2 = 729 cm^2  (2)

 

So....the area of the octagon is  (2) - (1)  =  567 cm^2 

 

It looks something like this :

 

 

 

 

cool cool cool

 Dec 4, 2018
edited by CPhill  Dec 4, 2018

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