Chapter 2.2, Problem 15MS

The enlarging area paradox (S). The square shown here has sides equal to 8 (a Fibonacci number) and thus has area equal to $8\times 8=64.$

The square can be cut up into four pieces whereby the short sides have lengths 3 and 5, as illustrated. (You will find these pieces in the kit that accompanied your book.) Now use those pieces to construct a rectangle having base 13 and height 5. The area of this rectangle is $13\times 5=65.$

So by moving around the four pieces, we increased the area by 1 unit! Using the puzzle pieces from your kit, do the experiment and then explain this impossible feat. Show this puzzle to your friends and record their reactions.