Tiling a Hall with an Alcove and a Recess
A community hall needs a new tiled floor. The main room is a rectangle 14.4 m by 9.6 m. A stage alcove opens off one long side; it is a rectangle 3.2 m by 2.4 m and its floor is tiled to match. A semicircular recess of radius 1.2 m is set into the opposite long wall and is also tiled. Tiles are 600 mm square, sold in boxes of four, at 18 units per box. The tiler budgets 10% extra for cutting waste on a straight lay. A decorative border strip 0.15 m wide runs along the four walls of the main rectangle only, measured on the outer edge; the alcove and recess openings are finished with separate trim and are excluded from the border. The border costs 11 units per metre. The committee has 3,000 units. One member proposes laying the tiles at 45 degrees 'to look more modern'; the tiler warns this would push waste to 18%.
1. Calculate the tiled area, the number of boxes needed at 10% waste, and the total cost including the border. Does it fit the budget?
Read the worked answer
Break the floor into three shapes.
- Main rectangle: 14.4 × 9.6 = 138.24 m²
- Alcove: 3.2 × 2.4 = 7.68 m²
- Semicircular recess: ½ × π × 1.2² = ½ × 3.14159 × 1.44 ≈ 2.26 m²
Total area = 138.24 + 7.68 + 2.26 = 148.18 m² (using π ≈ 3.14159).
With 10% waste: 148.18 × 1.10 = 163.00 m² of tile to buy.
Each tile is 0.6 × 0.6 = 0.36 m², so a box of four covers 1.44 m². 163.00 ÷ 1.44 = 113.19 boxes. You cannot buy 0.19 of a box, so order 114 boxes. Check: 113 boxes cover 162.72 m², which is 0.28 m² short, confirming the round-up.
Costs:
- Tiles: 114 × 18 = 2,052
- Border: perimeter of the main rectangle = 2 × (14.4 + 9.6) = 48 m; 48 × 11 = 528
- Total: 2,052 + 528 = 2,580
Budget remaining: 3,000 − 2,580 = 420 units.
2. The 45-degree proposal is put to a vote. Quantify its effect and advise the committee, considering both cost and risk.
Read the worked answer
At 18% waste the tile area becomes 148.18 × 1.18 = 174.86 m². 174.86 ÷ 1.44 = 121.4 boxes, so 122 boxes.
Cost: 122 × 18 = 2,196 for tiles, plus the unchanged 528 border = 2,724.
That is 144 units more than the straight lay, and it leaves only 3,000 − 2,724 = 276 units of contingency, compared with 420.
The cost alone is not decisive: 144 units is about 5% of the budget and the scheme is still affordable. The stronger objection is risk. A diagonal lay produces many more cut edges, especially along the 48 m border, and cut tiles break. The 18% figure is an allowance, not a guarantee; if it proves low, the committee is buying extra boxes mid-project, possibly from a different production batch with a visible shade difference. Diagonal layouts also make individual lipped or misaligned tiles more obvious, raising the chance of rework.
A defensible recommendation: keep the straight lay unless the aesthetic gain is a stated priority, and if the diagonal is approved, re-measure first and add one spare box (18 units) to the order rather than relying on the 18% allowance.
3. Before ordering, the committee checks the measurements. The 14.4 m length is confirmed, but the 9.6 m width was taken with a tape that may be 10 cm out either way. How sensitive is the order to that error, and what should be done?
Read the worked answer
Recompute with the width at 9.7 m and at 9.5 m, keeping the other shapes fixed.
Width 9.7 m: main area = 14.4 × 9.7 = 139.68; total = 139.68 + 7.68 + 2.26 = 149.62 m²; with 10% waste = 164.58 m²; 164.58 ÷ 1.44 = 114.29, so 115 boxes. That is one more box (+18 units).
Width 9.5 m: main area = 136.80; total = 146.74 m²; with 10% = 161.41 m²; 161.41 ÷ 1.44 = 112.09, so 113 boxes, one fewer.
So a 10 cm error moves the order by a full box in either direction. The rounding boundary is the reason: 148.18 × 1.1 lands almost exactly on 113.2 boxes, so small changes flip the integer.
The practical response is to re-measure the width properly before ordering, ideally at several points along the wall, because rooms are often not perfectly rectangular. If the diagonal lay is chosen, the same error compounds against an 18% allowance and a thinner budget buffer, making re-measurement even more important. Ordering the higher figure without checking risks paying for unused stock; ordering the lower risks a mid-job shortfall and a shade mismatch.