Scale drawings and maps · Year 8
In Year 8 you learn: map scales as ratios.
Maps, plans and models are drawn to scale: every length is the real length divided by the same number. A scale written as a ratio like 1 : 50,000 means 1 cm on the drawing is 50,000 cm in real life, using the same unit on both sides.
Key facts
- Real length = drawing length × scale number.
- Drawing length = real length ÷ scale number.
- In a ratio scale 1 : n both parts are in the same unit.
- Useful: 100 cm = 1 m and 100,000 cm = 1 km.
- Areas on a plan scale by the scale number squared, so convert lengths first, then work out the area.
Worked examples
Example 1
A map has a scale of 1 : 25,000. Two farms are 8 cm apart on the map. How far apart are they in real life?
Answer: 2 km
Example 2
A model car is built to a scale of 1 : 24. The real car is 4.2 m long. How long is the model?
Answer: 17.5 cm
Example 3
On a map, 3 cm represents 1.5 km. Write the scale in the form 1 : n.
Answer: 1 : 50,000