The simplest way to create your own tangram set is to print out a template.
You could print the diagram on card stock or other heavy paper, or use it as a template to cut the pieces out of cardboard, magnet paper, foam, etc.
Click here for the large template. (Roughly 7.5 inches or 20 centimeters square.)
Click here for the medium template. (Roughly 5 inches or 12.5 centimeters square.)
Click here for the small template. (Roughly 4 inches or 10 centimeters square.)