Convert between map or plan lengths and real lengths, write scales as ratios, and use them for areas and times.
What you will learn
- Use a map scale 1 : n
- Make and read scale drawings
- Write a scale as a ratio
- Work out real areas and journey times from a map
1 : n
A scale of 1 : 50,000 means 1 cm on the map is 50,000 cm in real life, which is 500 m.
- 4.2 cm on a 1 : 50,000 map
- 4.2 × 50,000 = 210,000 cm
- = 2,100 m = 2.1 km
Going the other way, divide: 3 km = 300,000 cm, and ÷ 50,000 gives 6 cm on the map. A model works the same way: at 1 : 40, a real 3.2 m wall is 320 cm ÷ 40 = 8 cm on the model.
To write a scale in the form 1 : n, put both lengths in the same unit, then divide by the first. "5 cm represents 2 m" is 5 cm : 200 cm = 1 : 40.
To choose a scale for a drawing, work out how big the real object would come out at each scale and pick the one that fits the paper and is not too small to see. A 30 m garden on 25 cm paper: at 1 : 100 it is 30 cm (too big); at 1 : 200 it is 15 cm (fits).
Map distances feed into other problems. A 12 cm walk on a 1 : 25,000 map is 12 × 25,000 = 300,000 cm = 3 km; at 4 km/h it takes 3 ÷ 4 = 0.75 hours = 45 minutes.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- 1 : n
- Straight-line distance
- Areas on a plan
7 practice questions, marked as you go; about 20 minutes in all.
Key terms
Pythagoras' theorem
In this unit: Constructions, loci and bearings
Three-figure bearings, scale drawings and maps, ruler-and-compass constructions, and loci: sets of points that follow a rule.
- Bearings
- Scale drawings and maps
- Constructions
- Loci