Practice Tiling Intuition in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Covering an entire surface with copies of one or more shapes that fit together perfectly with no gaps and no overlaps.
Bathroom tiles cover the floor perfectly—no gaps between them.
Example 1
easyCan regular pentagons tile the plane by themselves (no gaps or overlaps)? Explain using interior angles.
Example 2
mediumA kitchen floor 300\,\text{cm}\times 240\,\text{cm} is tiled with 20\,\text{cm}\times 20\,\text{cm} square tiles. How many tiles are needed? If tiles cost \$2.50 each, what is the total cost?
Example 3
easyWhich of these regular polygons can tile the plane on their own: equilateral triangle, regular hexagon, regular octagon? Explain using interior angles.
Example 4
mediumA wall 180\,\text{cm}\times 120\,\text{cm} is covered with rectangular tiles 15\,\text{cm}\times 10\,\text{cm}. How many tiles are needed? Verify using areas.