One day, when our miserly old landlord (from our former residence) was renovating the upstairs flat in order to charge twice as much for the mouldy appartment, I bravely sent my partner John upstairs to ask the nice Chippy (Aussie slang for carpenter) to cut my wooden square into the tangram shapes I had drawn on its surface. He kindly cut them, using his very loud circular saw. I undercoated the pieces and painted them black. Finally, I had my own proper tangram set.
It should be opaque and black, its easier to form the silhouettes that way. Cardboard isn't a permanent option as it will warp, but if you don't have a saw that can cut with fine precision, cardboard could be the way to go.
Here are some tangram designs for you to try. Some of the ducks are very amusing.
These images are taken from the book, Tangram: The Ancient Chinese Shapes Game by Joost Elffers, Penguin Books, 1979.
If you would like to try tangrams but find sissors a bit too dangerous try playing tangrams on-line, I prefer my wooden ones but this could be fun too, click here.