Garden Path Tiling: Area, Pack Sizes and a Tile Swap
The P5 classes are building a vegetable garden. The garden plot is a rectangle 6 m long and 4 m wide. A path 50 cm wide runs around the inside edge of the plot, and the remaining inner rectangle is filled with soil for planting. The path is to be paved with square tiles that are 25 cm by 25 cm, sold in boxes of 12 tiles. The caretaker has ordered 10 boxes, calculating that the path is about 9 m² and that "a box must cover roughly a square metre". Soil is sold in bags that each cover 0.75 m² of planting bed, and the classes want the bed filled to the correct depth with no bags wasted. The garden club also has the option of using 30 cm by 30 cm tiles, which are on sale at a lower price per tile, and the teacher wants to know whether that is a sensible swap.
1. Show that the path has an area of 9 m² and decide whether 10 boxes of 25 cm tiles are enough.
Read the worked answer
Outer rectangle: 6 × 4 = 24 m².
The path is 0.5 m wide on every side, so the inner rectangle is (6 − 2 × 0.5) × (4 − 2 × 0.5) = 5 × 3 = 15 m².
Path = 24 − 15 = 9 m² ✓
One tile = 25 × 25 = 625 cm². Path in cm² = 9 × 10,000 = 90,000 cm².
90,000 ÷ 625 = 144 tiles, and 144 ÷ 12 = 12 boxes exactly.
10 boxes give only 120 tiles, so the caretaker is 24 tiles (2 boxes) short. The error came from the rough "1 box ≈ 1 m²" estimate: each box actually covers 12 × 625 = 7,500 cm² = 0.75 m², so 9 m² needs 9 ÷ 0.75 = 12 boxes.
2. How many bags of soil are needed for the planting bed?
Read the worked answer
The planting bed is the inner rectangle, already found to be 15 m².
Each bag covers 0.75 m², so 15 ÷ 0.75 = 20 bags exactly.
Check: 20 × 0.75 = 15 m² ✓
Because soil is sold in whole bags, any area that is not an exact multiple of 0.75 m² would require rounding up - for example, 15.6 m² would need 21 bags. Here the numbers work out exactly, so there is no waste.
3. Would switching to 30 cm by 30 cm tiles be a sensible choice for this 50 cm path, even though they are cheaper per tile?
Read the worked answer
The deciding factor is how the tile width fits the 50 cm path.
With 25 cm tiles, 50 ÷ 25 = 2, so exactly 2 tiles span the path - almost every tile can be laid whole, with cutting needed only at the strip ends.
With 30 cm tiles, 50 ÷ 30 = 1.67, so a single tile is too narrow and two tiles make 60 cm, which is wider than the path. Every tile along the path would need cutting, and the offcuts are waste.
So the lower price per tile is misleading: more tiles are bought, more are cut and discarded, and more labour is needed. It is not a sensible swap unless the path width itself is redesigned to 60 cm.