6th Math Riddle 2019

Geometry Level 1

A point inside a square is connected to its four vertices, as shown.

What fraction of the square is shaded blue?

1 4 \frac 14 1 2 \frac 12 3 4 \frac 34 None of the above

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1 solution

Chew-Seong Cheong
Jan 11, 2019

If we draw two perpendicular lines through the point parallel to the sides of the square, we find that both the shaded and non-shaded regions have the same area of a + b + c + d a+b+c+d . Since the area of the square is 2 ( a + b + c + d ) 2(a+b+c+d) , the area of the shaded region is 1 2 \boxed{\frac 12} that of the square.

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