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Message: <blockquote data-quote="Randir" data-source="post: 12603283" data-attributes="member: 3497">SolutionThe key to the puzzle is the fact that neither of the 13×5 "triangles" is truly a triangle, because what would be the hypotenuse is bent. In other words, the hypotenuse does not maintain a consistent slope, even though it may appear that way to the human eye. A true 13 × 5 triangle cannot be created from the given component parts.The four figures (the yellow, red, blue and green shapes) total 32 units of area, but the triangles are 13 wide and 5 tall, so it seems, that the area should be  units. But the blue triangle has a ratio of 5:2 (=2.5:1), while the red triangle has the ratio 8:3 (≈2.667:1), and these are not the same ratio. So the apparent combined hypotenuse in each figure is actually bent.The amount of bending is around 1/28th of a unit (1.245364267°), which is difficult to see on the diagram of this puzzle. Note the grid point where the red and blue hypotenuses mate, and compare it to the same point on the other figure; the edge is slightly over or under the mark. Overlaying the hypotenuses from both figures results in a very thin parallelogram with the area of exactly one grid square, the same area "missing" from the second figure.<a href="http://en.wikipedia.org/wiki/Missing_square_puzzle" target="_blank">http://en.wikipedia.org/wiki/Missing_square_puzzle</a></blockquote>

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