Chessboard Chunks

On the right, you see a paper with a chessboard print on it. We want to cut the chessboard paper into pieces (over the lines!) such that each piece has twice as much squares of one color than of the other color (i.e. twice as much black squares as white squares or twice as much white squares as black squares). The Question: Is it possible to do this? Give a proof ! By  Rekha Ramalingam