Geometrical Puzzles


Square Intersection

To solve this puzzle just extend two sides of the large square as shown by the dotted lines in the illustration. This obviously divides the small square into four congruent parts. Since the small square has an area of 36 square units (6 x 6), the overlap (red quadrangle) must have an area of 36/4, or 9 square units. The amusing thing about the problem is that the area of overlap is constant regardless of the large square’s position as it rotates around A. The fact that BC is 4 units long is actually irrelevant information.

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Last Update
September 27, 2003

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