This problem is based on a tangram, but with the square cut into only 2 pieces:

Tangram consisting of a square cut into two pieces.

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape.

If you must match whole sides to each other so that the corners meet, how many new shapes can you make?

Watch out for shapes which are really the same but just turned round or flipped over.