What is a scale drawing?
A scale drawing shows a real object smaller or larger than it really is, while keeping the same shape. The scale is written as a ratio 1 : n, meaning 1 unit on the drawing stands for n identical units in real life.
Key idea
Actual length = drawing length × n. Drawing length = actual length ÷ n. Always change both measurements to the SAME unit first.
Converting lengths
Suppose a plan of a classroom uses the scale 1 : 200. A wall drawn 6 cm long represents 6 × 200 = 1200 cm, which is 12 m in real life. Going the other way, a real cupboard 3 m (300 cm) wide would be drawn 300 ÷ 200 = 1.5 cm wide.
Worked example
A map has scale 1 : 25 000. Two towns are 8 cm apart on the map. Actual distance = 8 × 25 000 = 200 000 cm = 2000 m = 2 km.
Areas on scale drawings
If lengths shrink by the factor n, areas shrink by n². For scale 1 : 100, an area of 6 cm² on the drawing represents 6 × 100² = 6 × 10 000 = 60 000 cm² = 6 m². This is why a small change in the scale ratio makes a big change in the real area, so always square the ratio, never just multiply by n.
To decide whether a scale reduces or enlarges, compare the two numbers. In 1 : n the drawing is smaller than the object when n is bigger than 1, and larger than the object when the scale is written the other way round, such as 5 : 1.
Remember
- 1 m = 100 cm, 1 km = 100 000 cm.
- Enlargement uses a scale like 5 : 1 (drawing bigger than object).
- Convert units before multiplying or dividing.