How can this "illegal geometry" problem be possible? Using 2 triangles each with base of 8 and height of 3, and 2 trapezoids with heights of 3 on top, 5 on bottom and height of 5, these four figures can create an area with 64 units squared. However, when rearranged as a rectangle with 13 x 5=65, one additional unit squared seemed to have been created. How is this possible?


This is a classic illusion based on the Fibonacci number identity
$$
13 \times 5 = 1 + 8 \times 8 .
$$
The "diagonal" of the rectangle isn't one. The slopes on each segment don't agree. There's one unit of  area between the "diagonals".
