Coaching Centre
Scale drawings, plans and elevations
Using a scale such as 1:100 to move between plan and real measurements, finding a scale, reading floor plans, site plans and elevations, and using them to find areas, volumes and costs.
Before anything is built, it is drawn. A floor plan is the view from directly above, a site plan shows the whole block of land, and an elevation is the view of one side, straight on. All of them are drawn to scale, so every length on paper stands for a real length. Read the scale correctly and you can price a kitchen floor before the builder arrives.
Working with a scale
$1$ unit on the plan represents $n$ of the same units in real life.
$\text{real length} = \text{plan length} \times n$ and $\text{plan length} = \text{real length} \div n$
Plans are measured in millimetres, so work in mm and convert to metres at the end. At $1 : 100$, $1$ mm on paper is $100$ mm $= 0.1$ m, so $10$ mm on paper is $1$ m.
On a $1 : 100$ floor plan, a bedroom measures $45$ mm by $38$ mm. Find its real dimensions and floor area.
A $12$ m wall is drawn $60$ mm long. What is the scale? How long would a $2.4$ m bench look on a $1 : 50$ plan?
Drag the yellow ends of the tape along the bottom wall of the house and check that $120$ mm on the plan is $12$ m. Tap Bed 1 and check its area using the plan sizes. Then switch to Bathroom $1 : 50$: why does a short real length look so big on this plan? On Block $1 : 200$, measure the gap between the house and the garage.
Plans and elevations
- Floor plan: walls as thick lines, doors as a gap with a quarter-circle showing the swing, windows as thin double lines in the wall. Dimensions are usually written in millimetres, for example $3800$.
- Site plan: the block boundary, the house footprint, driveways, and often a north arrow. Scales such as $1 : 200$ or $1 : 500$ are common.
- Elevation: a side view showing heights: walls, windows, roof pitch. A plan cannot show height, so elevations are needed for walls and volumes.
A front elevation shows a wall $4.5$ m long and $2.7$ m high, with a window $1.2$ m wide and $1.5$ m high. The wall needs $2$ coats of paint, and $1$ L covers $16$ m². How many $1$ L tins are needed?
On a $1 : 200$ site plan, a garage slab is $30$ mm by $30$ mm. It is $100$ mm thick and concrete costs $\$260$ per m³. Find the cost of the concrete.
Your turn
On a $1 : 100$ plan, a kitchen is $60$ mm by $30$ mm. Tiles cost $\$48$ per m². What do the tiles cost?
Show the working
Real size: $6$ m by $3$ m, so the area is $18$ m². Cost: $18 \times 48 = \$864$.
On a $1 : 100$ plan a wall is $45$ mm long. What is its real length, in metres?
$45 \times 100 = 4500$ mm $= 4.5$ m.
A $1 : 100$ plan shows a room $45$ mm by $38$ mm. What is the floor area, in m²?
Real: $4.5$ m by $3.8$ m. Area $= 4.5 \times 3.8 = 17.1$ m².
How long, in mm, is a $2.4$ m bench on a $1 : 50$ plan?
$2400 \div 50 = 48$ mm.
A $12$ m wall is drawn $60$ mm long. The scale is:
$12{,}000 \text{ mm} \div 60 \text{ mm} = 200$, so $1 : 200$.
Which drawing shows the height of a window?
Plans are views from above and can't show heights. An elevation is a side-on view.
A wall is $4.5$ m by $2.7$ m with a $1.2$ m by $1.5$ m window. What area, in m², is to be painted?
$12.15 - 1.8 = 10.35$ m².
Two coats are needed on $10.35$ m², and $1$ L covers $16$ m². How many $1$ L tins must be bought?
$20.7 \div 16 \approx 1.29$ L, so round up to $2$ tins.
A $1 : 100$ plan shows a kitchen $60$ mm by $30$ mm. Tiles cost $\$48$ per m². What is the cost, in dollars?
Real: $6$ m by $3$ m $= 18$ m². $18 \times 48 = 864$.
Exam style: On a $1 : 200$ site plan a slab is $30$ mm by $30$ mm, and it is $100$ mm thick. What volume of concrete, in m³, is needed?
$30 \times 200 = 6000$ mm $= 6$ m. Volume $= 6 \times 6 \times 0.1 = 3.6$ m³.
Exam style: Concrete costs $\$260$ per m³. What does the concrete for that slab cost, in dollars?
$3.6 \times 260 = 936$.