Square Deal

square regions puzzle

This unit square is divided into four regions by a diagonal and a line that connects a vertex to the midpoint of an opposite side. What are the areas of the four regions?

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a + b = 1/4, b + c = 1/2, and a + d = 1/2. Triangles a and c are similar, and c has twice the linear dimensions of a, so c = 4a. That’s enough to work out the areas: a = 1/12, b = 1/6, c = 1/3, and d = 5/12. From University of Toronto mathematician Ed Barbeau’s After Math (1995).

December 15, 2014December 21, 2014 | Puzzles