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The Missing Square |
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Answer to the Mysterious Square Problem
The pieces of the puzzle have an area of 32 square units.
Although they can be assembled to form what appears to be a 13×5 right triangle, they actually form quadrilaterals that are slightly smaller or slightly bigger than a 13×5 right triangle.
The top figure has an area of 32 square units. The bottom figure, including the empty square, has an area of 33 square units.
A real 13×5 right triangle would have an area of 32.5 square units. The distortion is difficult to see because one square of the picture is approximately 3% of the area.
The distortion can be seen more clearly when the empty square constitutes a larger percentage of the area, as in the figure below where 1 square represents 13% of the area.
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