Tiling a Rectangular Terrace
A homeowner wants to tile a rectangular terrace measuring 4.8 m by 3.6 m. The tiles are square, 40 cm on a side. The owner plans to buy tiles in boxes of 12 and wants a 10 % extra allowance for cutting waste, rounded up to whole boxes. A border strip 15 cm wide runs along the two long edges only, and the owner wonders whether this changes the count. The terrace must be fully covered with no gaps; cutting is allowed.
1. How many whole tiles cover the terrace if no waste allowance is applied?
Read the worked answer
Convert to cm: 480 cm × 360 cm. Tile side = 40 cm. Tiles along length: 480 / 40 = 12. Tiles along width: 360 / 40 = 9. Both divide exactly, so no cutting is needed: 12 × 9 = 108 tiles.
2. With a 10 % waste allowance, how many boxes of 12 must be bought?
Read the worked answer
Tiles needed with waste = 108 × 1.10 = 118.8 → round up to 119 tiles. Boxes = 119 / 12 = 9.916… → round up to 10 boxes. Check: 10 × 12 = 120 ≥ 119 ✓. So 10 boxes.
3. The 15 cm border along the two long edges is tiled with a different tile. What area does the border cover, in m²?
Read the worked answer
The border runs along both long edges (length 4.8 m each), width 0.15 m. Area per strip = 4.8 × 0.15 = 0.72 m². Two strips: 2 × 0.72 = 1.44 m². So the border covers 1.44 m², leaving 4.8 × 3.6 − 1.44 = 17.28 − 1.44 = 15.84 m² for the main tiles.