Phillip R. answered • 08/26/14

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the inscribed square forms a smaller right triangle on either side of it and an equilateral triangle on top of it.

If the shorter leg is x then the longer leg (and the length of a side of the square) is x√3

The base of the equilateral triangle then is made up of three segments x, x, and x√3 = (2 + √3)x

But we know the length of a side of the original triangle is 8(2√3 + 3).

If you solve for x and multiply by √3 to get the side of the square, you get 24

So the area is 576 square units