Scale Drawings
A scale drawing is an accurate, smaller or larger representation of a real object or place, where every length is in the same ratio to the real length, shown as a scale such as 1:50000 or 1 cm represents 2 m. GCSE questions use scale drawings with maps, plans and models, converting lengths and sometimes areas both ways.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the scale carefully, for example 1 : 20 or 1 cm represents 2 m, and note the units on each side.
- To find a real-life length from a scale drawing length, multiply the drawing length by the scale factor, the n in 1 : n.
- To find a scale drawing length from a real-life length, divide the real length by the scale factor.
- Make sure both lengths are in the same units before you multiply or divide, since a scale of 1 : n means the units on both sides must match.
- For area, remember the scale factor for area is the length scale factor squared, not the length scale factor itself.
- Convert your final answer into the units asked for in the question, for example from centimetres into metres or kilometres.
Worked example
A map has a scale of 1 : 50000. The distance between two towns on the map is 5.2 cm. Work out the real distance between the towns, in kilometres.
- Multiply the map distance by the scale factor: 5.2 x 50000 = 260000 cm.
- Convert centimetres to metres by dividing by 100: 260000 / 100 = 2600 m.
- Convert metres to kilometres by dividing by 1000: 2600 / 1000 = 2.6 km.
- State the final answer: the real distance is 2.6 km.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
A scale drawing of a model train uses a scale of 1:12. The real train carriage is 9.6 m long. Work out the length of the carriage on the scale drawing, in centimetres.
A rectangular office measures 6.4 m by 4.8 m in real life. A scale drawing is made using a scale of 1:80. (a) Work out the dimensions of the office on the scale drawing, in centimetres. (b) Work out the area of the office on the scale drawing, in cm^2.
On a scale drawing, a road that is 4.8 km long in real life is drawn as a straight line 6 cm long. (a) Write the scale of the drawing in the form 1:n. (b) Another road is 2.6 km long in real life. Work out the length of this road on the same scale drawing, in centimetres, giving your answer correct to 1 decimal place.
See real past-paper questions on scale drawings, organised by topic with official mark schemes →
Free printable worksheet
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