Question

Find the area of the shaded green square in the blue right triangle?

Answer 1

Both sides equal 6 and it's a right triangle: its other angles are 45° and so the blue triangles are similar: square and isocel.
Say x is the side length of the square, it's also the side of the two medium-size blue triangles.
So the long hypothenuse equals x+x+x=3x. According to Pythagore it's also equal to 6²+6²=72=(3x)²=9x²
Square area is thus x²=72/9=8

Comments

Ok this is not a good proof, I try again.