Triangles and are congruent right angled isosceles triangles. Squares blue and red are as shown. If the area of blue square is . What is the area of the red square?
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△ A B C can be split into 4 equal triangles and △ X Y Z can be split into 9 equal triangles
Since the blue square is 2 1 of the whole triangle, the area of the whole triangle is 2 ⋅ 1 8 9 = 3 7 8 .
Since the red square is 9 4 of the whole triangle, the area of the red square is 9 4 ⋅ 3 7 8 = 1 6 8 .