L-Shaped Room Materials Estimate
A student is refinishing an L-shaped study room before the term starts. The floor plan combines a 4.2 m by 3.0 m main rectangle with a 2.4 m by 1.8 m alcove; the alcove’s 2.4 m side is flush with part of the main room’s 4.2 m wall, so the shared edge is interior. The ceiling is 2.5 m high. There are two windows, each 1.2 m wide and 1.5 m high, and one door 0.9 m wide and 2.0 m high. Paint covers 10 m² per litre and is sold only in 4-litre cans at $38 each. Carpet costs $22 per square metre and must be purchased in whole square metres with an 8% waste allowance. Baseboard is sold in 2.4 m lengths at $9 each and is omitted across the door opening. The student plans one coat of paint unless the math forces a second can.
1. Compute the floor area, the carpet area to purchase including waste, and the carpet cost.
Read the worked answer
The main rectangle has area 4.2 × 3.0 = 12.6 m². The alcove has area 2.4 × 1.8 = 4.32 m². Total floor area = 12.6 + 4.32 = 16.92 m².
With an 8% waste allowance, the required carpet is 16.92 × 1.08 = 18.2736 m². Carpet is sold in whole square metres, so round up to 19 m². The cost is 19 × $22 = $418.
Note that rounding must happen after adding waste; using 16.92 m² and rounding before waste would under-order. The extra 0.7264 m² beyond the waste allowance is the unavoidable result of whole-square-metre purchasing.
2. Compute the paintable wall area, then determine how many 4-litre cans are needed for one coat and the paint cost.
Read the worked answer
The exterior perimeter of the L-shape is the sum of the two rectangle perimeters minus twice the shared 2.4 m edge: P = 2(4.2 + 3.0) + 2(2.4 + 1.8) - 2(2.4) P = 14.4 + 8.4 - 4.8 = 18.0 m.
Gross wall area = 18.0 × 2.5 = 45.0 m². Openings: two windows = 2 × 1.2 × 1.5 = 3.6 m²; door = 0.9 × 2.0 = 1.8 m². Total openings = 5.4 m². Net paintable area = 45.0 - 5.4 = 39.6 m².
At 10 m² per litre, one coat needs 39.6 / 10 = 3.96 L. A single 4-litre can covers 40 m², which is just enough. The paint cost is $38. If two coats were required, the need would be 7.92 L, forcing a second can.
3. Compute the baseboard length needed and the number of 2.4 m lengths to buy, then the cost. If the student instead buys 10% extra baseboard for cutting waste, does the number of lengths change?
Read the worked answer
The baseboard follows the same 18.0 m perimeter but stops at the door, so subtract the 0.9 m door width: 18.0 - 0.9 = 17.1 m.
Each length is 2.4 m: 17.1 / 2.4 = 7.125 lengths. Since lengths are sold whole, buy 8 lengths. Cost = 8 × $9 = $72.
With 10% extra for cutting waste: 17.1 × 1.10 = 18.81 m. Then 18.81 / 2.4 = 7.8375 lengths, which still rounds up to 8 lengths. The number of lengths and the cost do not change; the extra allowance is absorbed by the existing 8-length purchase.