Math Puzzle: Where is The Missing Square?

If you have already found answer to the missing area puzzle, you might want to try the mysterious missing square below. The largest triangle in the first figure is made up of two smaller triangles and two L-shaped polygons.

The largest triangle below (well, technically it’s not really a triangle) is also made up of the same polygons mentioned above.

The two large triangles have the same shape. But where did the missing square go?

If you think your eyes are playing tricks on you, I have created an  animated version of this puzzle here.  You would be able to see the animation only if Java is installed in your computer.