Practice Tessellation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A tessellation is a pattern that covers an infinite plane with repeated geometric shapes, leaving no gaps and having no overlaps.
Like a bathroom floor tile pattern that fits together perfectly and could extend forever in all directions.
Example 1
mediumExplain why regular hexagons tessellate the plane but regular pentagons do not.
Example 2
hardA proposed semi-regular tiling places 2 triangles and 2 squares at every vertex. Verify whether the vertex angles sum to 360°, and if not, find an arrangement of triangles and squares that does work.
Example 3
easyDoes an equilateral triangle tessellate the plane? Justify your answer using the interior angle.
Example 4
mediumA tiling uses regular octagons and squares. One proposed vertex arrangement has 1 octagon and 2 squares. Does this satisfy the 360° vertex condition? What arrangement actually works?