Break figure A into pieces, and you can put together a figure B out of the pieces if the figures have the...?

Question

Break figure A into some-sized pieces, and you can put together a figure B out of the pieces if the 2 figures have the same area. Prove this.

Thanks in advance!

Both figures are polygons.

Answer 1

This cannot be done. There is a famous problem called squaring the circle where you are supposed to cut up a circle and re-arrange the pieces into a square (naturally using all the pieces and getting the same area in the end).

But, it cannot be done. Here is a good discussion:

http://en.wikipedia.org/wiki/Squaring_the_circle