Congruency, Enlargement and Combined Transformations · 5.4.1
Meaning of tessellation
Students describe tessellation as a repeated pattern of one or more shapes that covers a flat surface completely, with no gaps and no overlaps between the shapes, usually generated by repeating a basic tile using isometric transformations.
The official learning standard (5.4.1)
“Explain the meaning of tessellation.”
What it means
Students describe tessellation as a repeated pattern of one or more shapes that covers a flat surface completely, with no gaps and no overlaps between the shapes, usually generated by repeating a basic tile using isometric transformations.
How it is examined
Mostly tested in Paper 1 with short objective items asking students to identify which pattern is a valid tessellation, or in Paper 2 with a brief written explanation linking the two conditions (no gaps, no overlaps) to a given diagram.
Worked example
A floor is covered completely by regular hexagonal tiles, with every tile fitting exactly against its neighbours. Explain whether this arrangement of hexagons is a tessellation, and state the two conditions that must be satisfied.
- A tessellation is a repeated arrangement of one or more shapes that covers a flat surface completely.
- Condition 1: there must be no gaps between the shapes.
- Condition 2: there must be no overlapping of the shapes.
- For the hexagonal tiling, the edges of neighbouring hexagons match exactly and the interior angles at each vertex add up to 360°, so both conditions are satisfied.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What is a tessellation?
A tessellation is a pattern made by repeating one or more shapes so that they cover a flat surface completely, with no gaps and no overlaps between the shapes.
Can more than one shape be used in a tessellation?
Yes. A tessellation can use a single repeated shape, such as squares or regular hexagons, or two or more different shapes arranged together, as long as there are still no gaps or overlaps.
How is tessellation related to transformations?
A tessellation is usually generated by repeatedly applying isometric transformations, translation, reflection and/or rotation, to a basic tile, since these transformations keep the shape and size unchanged so every copy fits together exactly.