Mathematics Standard • Year 12 • Ratios and rates • Lesson 3
Building Plans and Costs, Application
Take measurements off a plan, scale them up, find areas, then price the job. Also choose a scale that fits a given space, which is the part of "construct a scale drawing" that carries the marks.
1. Reading a floor plan
These measurements are taken from a house plan drawn at a scale of 1:100. Give the real dimensions and the floor area. 2 marks each
Q1.1 The lounge measures 6.2 cm by 4.5 cm on the plan.
Q1.2 The hallway measures 8.0 cm by 1.2 cm on the plan.
2. Costing the floor
Use your areas from section 1. 3 marks each
Q2.1 Timber flooring for the lounge costs $62 per square metre. Find the cost.
Q2.2 Vinyl for the hallway costs $28 per square metre. Find the cost.
3. Choosing a scale
Show the working for both directions, not just one. 3 marks
Q3.1 A block of land measures 40 m by 25 m. It must be drawn inside a box 16 cm by 10 cm. Find the smallest scale factor that will fit, then choose a friendlier scale and state the drawing's dimensions.
4. Map work, both directions
Both questions use a map with a scale of 1:100 000. 2 marks each
Q4.1 A cycling route measures 12.5 cm on the map. Find its real length in kilometres.
Q4.2 A highway is 21 km long. How long would it appear on the same map?
5. Multi-step, plan to price
Set out the whole chain: measure, scale, area, cost. 4 marks
Q5.1 On a plan drawn at 1:50, a rectangular deck measures 9.0 cm by 5.0 cm. Decking costs $95 per square metre. Find the real dimensions, the area, and the cost of the decking.
How did this worksheet feel?
What I'll revisit before next class:
Q1.1, The lounge
6.2 × 100 = 620 cm = 6.2 m, and 4.5 × 100 = 450 cm = 4.5 m. Area = 6.2 × 4.5 = 27.9 square metres.
Q1.2, The hallway
8.0 m by 1.2 m, so the area is 8.0 × 1.2 = 9.6 square metres.
Q2.1, Timber for the lounge
27.9 × 62 = $1729.80. Check: 1729.80 ÷ 62 = 27.9, the area we started with.
Q2.2, Vinyl for the hallway
9.6 × 28 = $268.80. Check: 268.80 ÷ 28 = 9.6.
Q3.1, Choosing a scale
Convert first: the block is 4000 cm by 2500 cm. Test both directions: 4000 ÷ 16 = 250 and 2500 ÷ 10 = 250, so 1:250 is the smallest factor that fits, and it fills the box exactly with no margin. A friendlier choice is 1:500, giving 4000 ÷ 500 = 8 cm by 2500 ÷ 500 = 5 cm, comfortably inside the box. Always round the scale factor up, never down, because rounding up shrinks the drawing further and it still fits.
Q4.1, The cycling route
12.5 × 100 000 = 1 250 000 cm = 12 500 m = 12.5 km. On a 1:100 000 map the centimetre reading happens to give the kilometre reading directly, which is worth noticing but worth proving too.
Q4.2, The highway
21 km = 2 100 000 cm, and 2 100 000 ÷ 100 000 = 21 cm. Check: 21 × 100 000 = 2 100 000 cm = 21 km.
Q5.1, Deck, plan to price
9.0 × 50 = 450 cm = 4.5 m, and 5.0 × 50 = 250 cm = 2.5 m [1]. Area = 4.5 × 2.5 = 11.25 square metres [1]. Cost = 11.25 × 95 = $1068.75 [2]. Check: 1068.75 ÷ 95 = 11.25.