Thursday, January 1, 2009

Overlapping Squares Puzzle Answer

In the diagram, the 4 in. square overlaps the 3 in. square in such as way that the corner of the larger square is at the center of the smaller square. The 4 in. square has been rotated so that its side trisects the side of the 3 in. square. What is the area of the shaded portion?

Rotate the 4” square until the sides of the squares meet at a right angle (dashed square above). We create a shaded triangle and a white triangle.

The triangles are congruent (properties of squares, the angles are congruent and the heights are both 1.5 and the bases are 0.5)

Take that small shaded triangle and move it to cover the small white triangle.

The area of the shaded region is congruent to one-fourth of the 3”square.
Area = 2.25

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