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?
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