It looks like this puzzle is based on a classic vanishing area paradox. I had some difficulty finding a good site that shows this one (most sites only show a triangular version of the paradox), and could only find the following site:
http://www.geocities.com/CapeCanaveral/ ... zzle1.html
The explanation it has is not correct.
Anyway, each side of the square has two triangular pieces along it, a large one and a short one. There are 2 solutions - all the edges can have a large triangle followed by a small one, or they all have a small one then a large one.
The paradox is that it seems that both solutions have the same square area, but in one of these solutions you will have a small piece left over. The reason is that the slopes of the triangles forming the outer edge of the square are not the same, so that in one solution the 'square' has bulging sides, in the other the 'square' has dented sides and you get a leftover piece.
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I don't know but it's worth a try.