A simpler version of the Missing Square Puzzle (depicted in the series of graphics below) uses four equal quadrilaterals and a small square, which form a larger square. When the quadrilaterals are rotated about their centers they fill the space of the small square, although the total area of the figure seems unchanged.
The apparent paradox is explained by the fact that the side of the new large square is actually a little smaller than the original one.
As simple and COOL as that.
Source: wikipedia.org
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