Why does rearranging the pieces of this triangle illusion give a different area? 
Possible Duplicate:
How come 32.5 = 31.5? 



If you count carefully, you'll see that the base is meant to be $13$ units long, while the height is $5$ units long. That means that the triangle on the top on the top figure, which has a height of $2$, should have a base of length $b$, where
$$\frac{b}{2} = \frac{13}{5}$$
or $b = \frac{26}{5}$, longer than the $5$ units depicted.
Likewise, the bottom red triangle, with a base of size $8$ should have a height of length $h$, with
$$\frac{h}{8} = \frac{5}{13}$$
or $h = \frac{40}{13}$, which is a little longer than the $3$ depicted.
So in fact, the "missing square" comes from misdrawing the pictures (or from having the individual figures drawn correctly, but the composed figures not being real triangles; the two inner triangles are not similar, though they "should" be). 
