The Extra Square

Strategies and Hints

  1. There are 64 square units in the square and 65 square units in the rectangle.

  2. Yes, the four pieces are identical in both the square and the rectangle.

  3. Students should discover that the four pieces do not fit together exactly to form the rectangle. There is actually a small "hole" along the diagonal.

  4. Student diagrams are shown below.

Solution

The long diagonal in the rectangle is not a line at all. It is actually a very skinny parallelogram with an area of 1 square unit.

Remarkably, you can use any set of three consecutive Fibonacci numbers to generate such figures.