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

1 Answer (Check Answer ▼)

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

answer Sep 16, 2015 by anonymous

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

commented Aug 28, 2016 by anonymous

Similar Puzzles

+1 vote

The given figure shows a triangle and a circle enclosed in a square. Find the area of the shaded parts.

The given figure shows a triangle and a circle enclosed in a square. Find the area of the shaded parts?

0 votes

A semicircle is inscribed in a right triangle as shown. What is the area of the shaded region in the figure?

0 votes

Construct a square. Construct 4 semicircles, each with diameter spanning...............what is the area shaded in blue?

Construct a square. Construct 4 semicircles, each with diameter spanning the center of the circle to a corner of the square and whose arc is counterclockwise from its diameter. Shade in blue the region exterior to the square but interior to the semicircles and interior to the square but exterior to the semicircles, as shown below. If the square has a side length equal to 4,
what is the area shaded in blue?