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Bunuel
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Bunuel

Two semi-circles are drawn on adjacent sides of a square with side length 1 as shown above. What is the area of the shaded region?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

Solution:

First, draw a diagonal from the upper left to the lower right of the square, creating two isosceles right triangles. Note that the two white regions in the upper right triangle, if they are combined, are identical to the shaded red lens-shaped figure in the lower left triangle. Thus, the shaded region is exactly half of the area of the square. Since a side of the square is 1, the area of the square is 1, and thus, the area of the shaded region is ½.

Answer: C
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