Scale Drawings and Maps
A scale drawing or map represents a real object or area at a reduced, or occasionally enlarged, size, with every length on the drawing standing for a fixed real length, written as a statement, such as '1 cm represents 2 m', or as a ratio, such as '1 : 200'. Working with a scale means converting confidently in both directions, turning a drawn length into a real-world distance, and a real-world distance into the length that should be drawn.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify how the scale is written: as a statement (for example, '1 cm represents 5 m') or as a ratio (for example, '1 : 500', where both numbers are in the same unit, usually cm).
- If the scale is a ratio like 1 : n, remember that 1 cm on the drawing represents n cm in real life - convert this into a more useful unit, such as m or km, once at the start.
- To find a real length from a drawn length, multiply the drawn (measured) length by the scale.
- To find a drawn length from a real length, divide the real length by the scale.
- Convert both measurements into the same unit before multiplying or dividing, and give the final answer in a sensible unit for its size (mm or cm for a small object, m or km for a distance).
- On a scale drawing of a floor plan or garden, use the same multiply-or-divide steps to find or check a real length, width or perimeter.
- If only two matching lengths are given (one drawn, one real) rather than a stated scale, divide the real length by the drawn length to work out the scale before using it.
Worked example
An architect's floor plan of a kitchen uses a scale of 1 : 50. On the plan, the kitchen is 12 cm long. Work out the real length of the kitchen, in metres.
- The scale 1 : 50 means every 1 cm on the plan represents 50 cm in real life.
- Multiply the drawn length by the scale: 12 x 50 = 600 cm.
- Convert to metres, since 600 cm is an awkward size to picture: 600 / 100 = 6 m.
- The real kitchen is 6 m long.
Practice questions
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Q1A garden design is drawn to a scale of 1 cm to 2 m. A path on the drawing measures 9 cm. Work out the real length of the path.Show answer
Answer: 18 m (9 x 2)
Q2A model aeroplane is built to a scale of 1 : 48. The wingspan of the real aeroplane is 14.4 m. Work out the wingspan of the model, in cm.Show answer
Answer: 30 cm (14.4 m = 1440 cm, then 1440 / 48)
Q3A street map has a scale of 1 cm to 300 m. The distance from a school to a library on the map is 5.5 cm. Work out the real distance, in km.Show answer
Answer: 1.65 km (5.5 x 300 = 1650 m)
Q4A wildlife park map uses a scale of 1 : 25000. The distance between the entrance and the lion enclosure on the map is 4 cm. Work out the real distance, in km.Show answer
Answer: 1 km (4 x 25000 = 100000 cm, which equals 1 km)
Q5A blueprint of an office building uses a scale of 1 cm to 4 m. A corridor in real life is 34 m long. Work out the length of the corridor on the blueprint.Show answer
Answer: 8.5 cm (34 / 4)
Q6A hiking map uses a scale of 1 cm to 1.5 km. A circular trail is 18 km long in real life. Work out the length of the trail as drawn on the map.Show answer
Answer: 12 cm (18 / 1.5)
Q7A tourist map of a town centre does not state its scale. A road that is known to be 250 m long measures 5 cm on the map. Work out the scale of the map, giving your answer in the form '1 cm to ___ m'.Show answer
Answer: 1 cm to 50 m (250 / 5)
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A scale model of a shipping container is built at a scale of 1 : 25. (a) The real container is 6 m long. Work out the length of the model, in cm. (b) The model has a height of 10.4 cm. Work out the real height of the container, in metres.
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A cartographer is drawing a new map of a nature reserve at a scale of 1 cm to 750 m. (a) A boardwalk in the reserve is 3.6 km long. Work out the length the cartographer should draw on the map, in cm. (b) A pond is drawn with a diameter of 2.4 cm on the map. A visitor estimates the real diameter of the pond is about 240 m. Is the visitor's estimate reasonable? Show a calculation to support your answer.
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Free printable worksheet
Want more practice on paper? Download the scale drawings and maps worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 39 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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