Tiling Intuition Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
A wall 180 cm×120 cm180\,\text{cm}\times 120\,\text{cm} is covered with rectangular tiles 15 cm×10 cm15\,\text{cm}\times 10\,\text{cm}. How many tiles are needed? Verify using areas.

Solution

  1. 1
    Step 1: Tiles along length: 180/15=12180/15 = 12. Tiles along height: 120/10=12120/10 = 12. Total: 12×12=14412 \times 12 = 144 tiles.
  2. 2
    Step 2: Area check: wall area =180×120=21,600= 180 \times 120 = 21{,}600 cm2^2. Tile area =15×10=150= 15 \times 10 = 150 cm2^2. Number =21,600/150=144= 21{,}600/150 = 144 ✓.

Answer

144144 tiles.
When tiles fit evenly (no cuts needed), dividing the wall area by the tile area gives the count. Alternatively, count along each dimension and multiply. Both methods must agree — a useful check for tiling problems.

About Tiling Intuition

Covering an entire surface with copies of one or more shapes that fit together perfectly with no gaps and no overlaps.

Learn more about Tiling Intuition →

More Tiling Intuition Examples

Example 1 easy

Can regular pentagons tile the plane by themselves (no gaps or overlaps)? Explain using interior ang

Example 2 medium

A kitchen floor [formula] is tiled with [formula] square tiles. How many tiles are needed? If tiles

Example 3 easy

Which of these regular polygons can tile the plane on their own: equilateral triangle, regular hexag

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