Estimating Quantities & Costs from Plans
Use plans to estimate materials and costs for NSW Year 12 Mathematics Standard 1 (NESA outcome MST-12-S1-05). Before buying tiles, paint, turf or fencing, you take measurements from a scale drawing and turn them into real lengths, areas and perimeters.
You will use the real area for things that cover a surface and the real perimeter for things that run around the edge, work out how many tins, boxes or rolls to buy (rounding up), and calculate and compare costs — practical for home projects and trade jobs.
Theory
To estimate materials and costs from a plan, turn every plan length into a real length, then find the area or the perimeter, and finally multiply by the price or divide by what one tin or roll covers. This Year 12 Standard 1 (NSW) guide shows how to price flooring, paint, turf and fencing.
To estimate materials from a plan, first use the scale to change every plan length into a real length: real length \(=\) scale factor \(\times\) plan length, then \(\text{mm}\div1000\) for metres. Going back, plan length \(=\) real length in mm \(\div\) scale factor, for example \(6.2\text{ m}=6200\text{ mm}\) and \(6200\div100=62\text{ mm}\) at \(1:100\).
Things that cover a surface (tiles, carpet, turf, paint, sealer) need the area in \(\text{m}^2\), and cost \(=\) area \(\times\) price per \(\text{m}^2\). Things that go around the edge (fencing, skirting board) need the perimeter in \(\text{m}\), and cost \(=\) length \(\times\) price per metre. Leave out any side that is not needed.
The number of items \(=\) amount needed \(\div\) amount one item covers. If this is not a whole number, round up. Two coats of paint need twice the area. This is a core Year 12 Standard 1 (NSW) Ratios and rates skill.
Change each plan length to a real length with the scale factor \(x\):
Cost of covering a surface, or of going around the edge:
Number of tins, boxes or rolls (always round up):
How to estimate quantities and costs from a plan
- Scale each plan length to a real length in metres.
- Decide whether the job needs an area (covering) or a perimeter (edging), and leave out any side not needed.
- Calculate the area or perimeter, doubling for two coats if needed.
- Finish: divide by the coverage and round up for items, or multiply by the price for the cost.
Find the real sides, then the area, then the cost.
| \(\text{length}\) | \(=\) | \(100 \times 75\text{ mm} = 7.5\text{ m}\) |
| \(\text{width}\) | \(=\) | \(100 \times 40\text{ mm} = 4\text{ m}\) |
| \(A\) | \(=\) | \(7.5 \times 4 = 30\text{ m}^2\) |
| \(\text{cost}\) | \(=\) | \(30 \times \$30\) |
| \(\therefore\ \text{cost}\) | \(=\) | \(\$900\) |
The vinyl costs \(\$900\).
Find the real sides, then add only the sides that need fencing.
| \(\text{length}\) | \(=\) | \(200 \times 30\text{ mm} = 6\text{ m}\) |
| \(\text{width}\) | \(=\) | \(200 \times 20\text{ mm} = 4\text{ m}\) |
| \(\text{fence}\) | \(=\) | \(6 + 4 + 4 = 14\text{ m}\) |
| \(\text{cost}\) | \(=\) | \(14 \times \$40\) |
| \(\therefore\ \text{cost}\) | \(=\) | \(\$560\) |
The fencing costs \(\$560\).
Find the area, double it for two coats, divide by the coverage and round up.
| \(\text{length}\) | \(=\) | \(50 \times 120\text{ mm} = 6\text{ m}\) |
| \(\text{height}\) | \(=\) | \(50 \times 54\text{ mm} = 2.7\text{ m}\) |
| \(A\) | \(=\) | \(6 \times 2.7 = 16.2\text{ m}^2\) |
| \(\text{two coats}\) | \(=\) | \(2 \times 16.2 = 32.4\text{ m}^2\) |
| \(\text{tins}\) | \(=\) | \(32.4 \div 10 = 3.24 \ \Rightarrow\ 4\) |
| \(\therefore\ \text{cost}\) | \(=\) | \(4 \times \$52 = \$208\) |
\(4\) tins are needed, costing \(\$208\).
Find the real area, cost each option, then subtract.
| \(\text{length}\) | \(=\) | \(500 \times 36\text{ mm} = 18\text{ m}\) |
| \(\text{width}\) | \(=\) | \(500 \times 24\text{ mm} = 12\text{ m}\) |
| \(A\) | \(=\) | \(18 \times 12 = 216\text{ m}^2\) |
| \(\text{Turf A}\) | \(=\) | \(216 \times \$9.50 = \$2052\) |
| \(\text{Turf B}\) | \(=\) | \(216 \times \$11 = \$2376\) |
| \(\therefore\ \text{saving}\) | \(=\) | \(\$2376 - \$2052 = \$324\) |
Choosing Turf A saves \(\$324\).
Common pitfalls
Frequently asked questions
How do you estimate the cost of flooring from a plan?
Use the scale to change each side of the room into real metres, multiply them to get the floor area in square metres, then multiply by the price per square metre. A 7.5 m by 4 m room is 30 square metres, so at $30 per square metre the flooring costs $900.
When do you use area and when do you use perimeter?
Use area for anything that covers a surface, such as tiles, carpet, turf or paint, because these are priced per square metre. Use perimeter for anything that goes around the edge, such as fencing or skirting board, because these are priced per metre.
How many tins of paint do I need?
Find the area to be painted, multiply by the number of coats, then divide by the area one tin covers. Always round up to the next whole tin. For 32.4 square metres with tins that cover 10 square metres, 32.4 divided by 10 is 3.24, so you need 4 tins.
Why do you round up when buying materials?
Shops sell whole boxes, tins and rolls. If you need 3.24 tins you would run out with 3, so you must buy 4, even when the decimal part is small.
Can you multiply the plan area by the scale factor?
No. The scale factor applies to lengths, not areas. Change each side to its real length first, then multiply the real lengths to get the real area.