Quarters

Weekly Problem 27 - 2014
Four congruent isosceles trapezia are placed in a square. What fraction of the square is shaded?
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Quarters


Four congruent isoceles trapeziums are placed so that their longer parallel sides form the diagonals of a square PQRS, as shown. The point X divides PQ in the ratio 3:1. What fraction of the square is shaded?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.