Scale Drawings & Building Plans
Read building plans and other scale drawings for NSW Year 12 Mathematics Standard 1 (NESA outcome MST-12-S1-05). A building plan shows a real house with every length shrunk by the same factor — at \(1:100\), each 1 mm on the plan is 100 mm in the real building.
You will take measurements off a plan and turn them into real lengths, recognise the usual symbols for doors and windows, tell a floor plan from an elevation, and find real perimeters and floor areas — useful when renovating, renting or fitting furniture into a room.
Theory
A building plan is a scale drawing: with a scale of \(1:100\), every \(1\text{ mm}\) on the plan is \(100\text{ mm}\) in the real building. This Year 12 Standard 1 (NSW) guide shows how to turn plan lengths into real lengths, read the door and window symbols, and find real perimeters and floor areas.
A scale drawing shows a real object with every length shrunk by the same amount. On a plan with scale \(1:x\), the number \(x\) is the scale factor: \(1\text{ mm}\) on the plan is \(x\text{ mm}\) in reality. Plans are usually measured in millimetres, so divide by \(1000\) to get metres.
A scale can also be written in two units, such as \(1\text{ cm}:2\text{ m}\). This means each \(1\text{ cm}\) on the plan is \(2\text{ m}\) in reality, so the real length in metres is the plan length in centimetres \(\times 2\).
A floor plan is the view of a building from above. An elevation is the view of one wall from the side, so it shows heights. On a floor plan, a gap in a wall with a quarter-circle is a doorway, and thin parallel lines drawn along a wall, in a break in the wall, are a window. This is a core Year 12 Standard 1 (NSW) Ratios and rates skill.
On a plan with scale \(1:x\), turn a plan length into a real length by multiplying by the scale factor:
To go the other way (real to plan), change the real length to millimetres and divide by the scale factor:
For example at \(1:100\), \(8.5\text{ m}=8500\text{ mm}\) and \(8500\div 100=85\text{ mm}\).
Change millimetres to metres by dividing by \(1000\):
For a rectangular room, use the real side lengths:
How to find real measurements from a plan
- Read the scale and note the scale factor (or what \(1\text{ cm}\) stands for).
- Measure or read each length you need from the plan.
- Multiply each plan length by the scale factor, then convert to metres (\(\text{mm}\div 1000\)).
- Calculate the perimeter or area from the real lengths, and give the answer with units.
Multiply by the scale factor \(50\), then change millimetres to metres.
| \(\text{real length}\) | \(=\) | \(50 \times 64\text{ mm}\) |
| \(\) | \(=\) | \(3200\text{ mm}\) |
| \(\) | \(=\) | \(3200 \div 1000\) |
| \(\therefore\ \text{real length}\) | \(=\) | \(3.2\text{ m}\) |
The wall is \(3.2\text{ m}\) long.
Each \(1\text{ cm}\) on the plan stands for \(2.5\text{ m}\), so multiply by \(2.5\).
| \(\text{real length}\) | \(=\) | \(4.4 \times 2.5\) |
| \(\therefore\ \text{real length}\) | \(=\) | \(11\text{ m}\) |
| \(\text{check: } 11 \div 2.5\) | \(=\) | \(4.4\text{ cm}\) |
The path is \(11\text{ m}\) long.
Convert each side to metres, then add around the rectangle.
| \(\text{length}\) | \(=\) | \(200 \times 35\text{ mm} = 7\text{ m}\) |
| \(\text{width}\) | \(=\) | \(200 \times 20\text{ mm} = 4\text{ m}\) |
| \(P\) | \(=\) | \(2(7+4)\) |
| \(\therefore\ P\) | \(=\) | \(22\text{ m}\) |
The real perimeter is \(22\text{ m}\).
A gap in a wall is a doorway. Convert every length with the factor \(100\).
| \(\text{(i) door}\) | \(=\) | \(100 \times 9\text{ mm} = 0.9\text{ m}\) |
| \(\text{length}\) | \(=\) | \(100 \times 48\text{ mm} = 4.8\text{ m}\) |
| \(\text{width}\) | \(=\) | \(100 \times 32\text{ mm} = 3.2\text{ m}\) |
| \(\text{(ii) }A\) | \(=\) | \(4.8 \times 3.2\) |
| \(\therefore\ A\) | \(=\) | \(15.36\text{ m}^2\) |
(i) A doorway \(0.9\text{ m}\) wide; (ii) the floor area is \(15.36\text{ m}^2\).
Common pitfalls
Frequently asked questions
What does a scale of 1:100 mean on a building plan?
It means every 1 unit on the plan is 100 of the same units in the real building. So 1 mm on the plan is 100 mm in real life, and 1 cm on the plan is 100 cm, which is 1 m.
How do you find the real length from a building plan?
Measure the length on the plan, multiply by the scale factor, then change the units. A wall drawn 64 mm long at a scale of 1:50 is 64 times 50, which is 3200 mm. Divide by 1000 to get 3.2 m.
What does a scale like 1 cm : 2.5 m mean?
It means each 1 cm on the plan stands for 2.5 m in reality, so multiply the plan length in centimetres by 2.5 to get the real length in metres. A path drawn 4.4 cm long is 4.4 times 2.5, which is 11 m.
How do you find the real floor area from a plan?
Change each side to its real length in metres first, then multiply. A study drawn 48 mm by 32 mm at 1:100 is 4.8 m by 3.2 m, so its floor area is 4.8 times 3.2, which is 15.36 square metres.
How do you show a door and a window on a floor plan?
A doorway is drawn as a gap in the wall with a quarter-circle showing how the door swings. A window is drawn as thin parallel lines along the wall, in a break in the wall.
What is the difference between a floor plan and an elevation?
A floor plan is the view looking straight down from above and shows the layout and sizes of the rooms. An elevation is the view of one wall from the side and shows heights, such as how tall the doors and windows are.