Hexagonal tangrams

How many different hexagons can be made from a tangram?

You can download a tangram that can be printed and cut into seven pieces.

Students use translation, rotation and reflection to experiment with the tangram pieces. They must use all seven pieces and are allowed to flip the parallelogram over. There are four different convex hexagons. Here is one.

A convex hexagon made from a tangram.

Can they find the other three? Encourage students to draw them or take photos.

Students will inevitably find that some of their solutions are in fact congruent to others, although they may look different due to their orientation or the arrangement of the pieces within the shape.

How many non-convex hexagons can be made using all seven pieces of the tangram? Again the parallelogram can be flipped over and students should draw their hexagons or take photos. They might want to name them!

A non-convex hexagon that looks like a garden gnome.

You can download the Tangram hexagons: Student worksheet and the Tangram hexagons: Answers.