Monday, May 24, 2010

Overlapping Squares Puzzle

Overlapping Squares

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?

answer, here, in a backdated post.


  1. I squared off the shaded part in the 3" square to create a rectangle that was 1.5" x 2". Then, I figured out that the unshaded parts of that rectangle were two triangles 1.5" x 0.5" (or 0.75 sq. in. total). That meant that the shaded area was (2)(1.5)-0.75 = 2.25 sq. in. Is that right?

  2. That makes sense to me. I figured if you had overlapped them so that one corner of the large square was placed on the center of the small square, then the area of overlap was 1.5 X 1.5 = 2.25 in^2. So then if you rotate it, you gain an additional triangular piece, but lose the same sized triangular piece so the area of overlap would still be 2.25 in^2. I don't know if that is a good way to look at it or not.

  3. Sorry! I mean if you start out by overlapping them so the corner of the large one is on the center of the small one and the edges are parallel/perpendicular ... and then rotate it.