Tiling a Community Hall Floor on a Budget
A rectangular community hall measures 12.5 m by 8.4 m. The committee wants to tile the floor with square tiles of side 40 cm, leaving a 1.2 m wide strip along one 12.5 m wall untitled for a stage. Tiles are sold in boxes of 12 and cost $34.50 per box. A 5% allowance for cutting waste is required, and the supplier only sells whole boxes. The committee has a budget of $2,400. A member proposes laying tiles diagonally 'to use fewer tiles', and another asks whether the 40 cm tiles will divide the room dimensions exactly.
1. Calculate the tiled area, the number of tiles needed including the 5% waste allowance, and the number of boxes required.
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Tiled region: the stage strip runs along one 12.5 m wall, so the tiled rectangle is 12.5 m by (8.4 - 1.2) = 12.5 m by 7.2 m.
Area = 12.5 x 7.2 = 90 m squared.
Tile area = 0.4 m x 0.4 m = 0.16 m squared.
Tiles = 90 / 0.16 = 562.5, so 563 whole tiles before waste.
With 5% waste: 562.5 x 1.05 = 590.625, round up to 591 tiles.
Boxes = 591/12 = 49.25, so 50 boxes (whole boxes only).
Check: 50 boxes give 600 tiles, which is 9 extra above the 591 needed, a sensible buffer.
2. Compute the total cost and determine whether the budget is met. Then assess the suggestion to lay tiles diagonally.
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Cost = 50 boxes x $34.50 = $1,725.
Budget is $2,400, so the project is within budget with $675 to spare (28% of budget remaining).
Diagonal laying does not reduce the number of tiles: the floor area is fixed and each tile covers the same 0.16 m squared regardless of orientation. What diagonal laying does change is the cut pattern: it produces many triangular edge cuts, which typically increases waste well beyond 5%, perhaps to 10-15%. At 12% waste the tile count would be 562.5 x 1.12 = 630, i.e. 53 boxes, costing $1,828.50, still within budget but $103.50 more.
The judgement is that diagonal laying is a design choice with a real cost premium, not a saving, and the 5% waste allowance would need revising if it were adopted.
3. Another member asks whether 40 cm tiles divide the room dimensions exactly. Check both the 12.5 m length and the 7.2 m tiled width, and state the practical consequence.
Read the worked answer
Convert to centimetres: length 1250 cm, tiled width 720 cm.
Length: 1250 / 40 = 31.25, so 31 full tiles plus a 10 cm strip. Not exact.
Width: 720 / 40 = 18 exactly, so 18 full tiles fit with no cutting along that direction.
Consequence: every row needs a 10 cm cut tile at one end, i.e. 18 cut tiles along the length (one per row), each cut from a 40 cm tile and leaving a 30 cm offcut that is generally unusable. That is 18 extra tiles consumed beyond the 31 x 18 = 558 full-tile grid, giving 576 tiles, and the 5% waste allowance (591) still covers it.
An alternative worth raising is starting with a half-tile at each end, which uses the offcuts from both sides and looks more balanced, but it does not reduce the total tile count.