Tessellation

Free interactive math game: Tessellation — Which shape tiles?. Part of the Geometric Shapes category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. Which shape can tessellate the plane (cover it without gaps)?
  2. Which shape can tessellate the plane (cover it without gaps)? — 4, 3, 2, 5
  3. Which shape can tessellate the plane (cover it without gaps)? — 5, 3, 4, 0
  4. Which shape can tessellate the plane (cover it without gaps)? — 4, 5, 1, 3

About this exercise

Which shapes tile a flat surface with no gaps and no overlaps.

How to solve it

Look at the angles meeting at a corner. They have to add to exactly 360 degrees, because a full turn is what closes the gap around a point.

Worked example

Regular hexagons tessellate because three of their 120-degree angles meet at 360 exactly.

Common mistake

Assuming every regular polygon tiles. A pentagon has 108-degree angles, and no whole number of those reaches 360, so gaps are unavoidable.