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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 60 centimeters. What is the number of square centimeters in the area of the octagon?

 Apr 22, 2022
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If the  perimeter of the square =  60, then each side = 15

 

The area of the square  =  15^2  = 225

 

And we have 4 congruent  right triangles with legs = 5  formed  outside the octagon but inside the square

 

The  area  of each = (1/2)(5)^2  =  25 / 2

 

So  their  combined area  = 4 * 25  / 2  =  50

 

So  the area of the octagon =   225  -  50  =    175 

 

cool cool cool

 Apr 22, 2022
edited by CPhill  Apr 22, 2022

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