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another way to look at it:
if the top large triangle was a real triangle, it would have area 13*5/2 = 32.5.
The pieces have area 12, 8, 7, and 5. The sum of this is 32. Hence, .5 of a square's area would need to be added to this shape to make it a true triangle. This area would be along the slightly-bent hypotenuse.
In the second shape, the hypotenuse is bent outwards, occupying an extra .5. It is the difference between lacking .5 and having .5 too much that allows the empty square.
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