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

What fraction of the square is shaded blue?

$\frac 14$
$\frac 12$
$\frac 34$
None of the above

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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 $a+b+c+d$ . Since the area of the square is $2(a+b+c+d)$ , the area of the shaded region is $\boxed{\frac 12}$ that of the square.