Tricky Colors

Geometry Level 1

$ABCD$ is a square with $M$ , $N$ , $O$ , and $P$ being the midpoints of their respective sides.

Which of the following has a larger area inside the square: the shaded (green) region or the non-shaded (white) region?

The green region The white region They are equal

2 solutions

Pi Han Goh
Aug 24, 2016

Relevant wiki: Composite Figures

By rearranging the pieces, we can see the area covered by the shaded region and the non-shaded region are equal.

thanks bro ..

Ajay Sambhriya - 4 years, 9 months ago

Michael Mendrin
Aug 24, 2016

Let the vertices of the center square be $1,2,3,4$ , clockwise from the green right triangle with vertices $P,D$ . Then, by symmetry, quadrilaterals $D14O = C43N$ . Swap the colors so that quadrilateral $ANCP$ is all white. The area of $ANCP$ is obviously $\dfrac{1}{2}$ of the square $ABCD$ .

Tricky Colors

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