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Shaded Square

Problem

The top left corner of a square is joined to the midpoint of the bottom edge, the midpoint of the top edge is joined to the bottom right corner; the top right corner is joined to the midpoint of the left edge, and the midpoint of the right edge is joined to the bottom left corner.


What fraction of the square is shaded?


Solution

Consider the following diagram.


By symmetry it should be clear that each triangle is congruent. Hence 4/20 = 1/5 of the square is shaded.

Problem ID: 228 (10 Jul 2005)     Difficulty: 1 Star

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