ThePerfectFlaw

Another way you can tell there's something fishy going on with this triangle is to do the math. Just by going by the points involved and not paying attention to the lines, the area of the triangle should be 32.5 units ((5x13)/2)

However, if you add up the individual sections, again just going by points which seem to line up neatly, You get a discrepancy.

For the top triangle. The teal triangle is 5 units. The red is 12 units. The green is 8 and the orange is 7. 12+8+7+5 = 32 units.

For the bottom triangle, you have the same four shapes just going by points (again ignoring the lines). However, you toss in the little white square, and suddenly get a shape that is 33 units big.

32, nor 33 is not, in my book at least, equal to 32.5, so something fishy is going on. The bent Hyp. explains this. The mean of the two triangles is 32.5 however.

The base is the same, and the height is the same in both shapes.

However, if you were to straighten out the Hyp, you would find that the red triangle and the teal triangle are not as symmetrical, nor as 'cute' as the image leads you to believe.

Anterak

Even easier :
Take the blue one, and count the base length : 5 units.
Take the red one, count from left 5 units, and get a vertical line to make another triangle. You see you don't get the same height with the normal blue (2 units) and the shorter red (2.5 units).

Hypothenus in both cases are bent, one concave(sp) and one convexe(sp too, my english is poor). Surface between them represents (as Zehn explained) the "missing" square.

ThePerfectFlaw

I'm such a nerd.