A map has a scale of 1 : 40 000. A lake is 6 cm long on the map. Find the real length of the lake in kilometres.
- Real length = 6 × 40 000 = 240 000 cm.
- Change to metres: 240 000 ÷ 100 = 2400 m.
- Change to kilometres: 2400 ÷ 1000 = 2.4.
Answer: 2.4 km
Scale drawings
Maths · Geometry. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
A scale tells you how a drawing or map compares with real life. A scale of 1 : 50 000 means that 1 cm on the map stands for 50 000 cm in real life, which is 500 m or 0.5 km. Multiply by the scale to go from the map to real life, and divide to go from real life to the map. Then change the units.
A bearing gives a direction as an angle. It is measured from north, clockwise, and is written with three figures, such as 045° or 210°.
The words matter: the bearing of B from A is measured at A. The bearing back from B to A differs by 180°.
Rules to remember
- Scale 1 : n: real length = map length × n; map length = real length ÷ n
- 100 cm = 1 m and 100 000 cm = 1 km, so 1 : 50 000 means 1 cm represents 0.5 km
- Areas use the scale squared: if 1 cm represents 0.5 km, then 1 cm2 represents 0.5 × 0.5 = 0.25 km2
- Bearing: start at north, turn clockwise, write three figures (7° is written 007°)
- North 000°, east 090°, south 180°, west 270°; north-east 045°, south-east 135°, south-west 225°, north-west 315°
- Back bearing: add 180° if the bearing is less than 180°, subtract 180° if it is more (110° → 290°, 250° → 070°)
Common mistake
Students measure the bearing at the wrong point or turn anticlockwise. For the bearing of B from A, stand at A, face north and turn clockwise until you face B.
Worked example
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