Parallelogram Dissection Paradox

move red triangle

move green triangle

3×13 = ?

This Demonstration shows a dissection paradox. On one hand, the area of the parallelogram is

3×13=39

, and on the other hand, the area of the rectangle is

5×8=40

. An explanation is in the Details section.

The red and blue diagonals and the green and brown diagonals are not parallel, so the figure is not a parallelogram. The slopes of the diagonals are

3/8

and

2/5

with a difference of

1/40

, which is almost imperceptible.

Izidor Hafner