Scale drawings and real distances
Convert between diagram lengths and real distances with consistent units.
Core and Extended.
Before you begin
- Convert between centimetres, metres and kilometres.
- Multiply and divide ratios.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How many centimetres are in 2 metres?
What you will learn
- Interpret ratio and statement scales.
- Draw a plan to a specified scale.
- Convert a measured diagram length into a real distance.
A scale compares like units
The scale 1 : 50 000 means one diagram unit represents 50 000 of the same real unit. One centimetre therefore represents 50 000 cm = 500 m = 0.5 km. Multiply a diagram length by the scale factor to find the real length; divide a real length by the factor to find its diagram length, after converting to matching units.
A statement such as 1 cm represents 2 m already gives two different units explicitly. A 3.5 cm diagram length then represents 7 m. Do not treat this statement as the ratio 1 : 2; its equivalent ratio is 1 : 200 after converting metres to centimetres. Write the conversion before using a calculator.
Draw and interpret a scaled plan
For a 12 m by 8 m room at 1 : 200, convert the lengths to 1200 and 800 cm, then divide by 200. Draw a 6 cm by 4 cm rectangle with a ruler, preserving the right angles. Label the scale, dimensions and units so another person can recover the real lengths.
To measure an irregular route, add the lengths of its separate straight segments before converting. Curved routes need an appropriate measurement method and are only approximate. Printed or onscreen diagrams can be resized, so a quoted scale is reliable only at the intended print size; a scale bar resizes with the diagram. Use supplied measurements when a diagram is labelled not to scale.
Pause and explain
At 1 : 200, a real length of 8 m is drawn as what?
Worked example
On a map at 1 : 50 000, two places are 7.6 cm apart. Find their real straight-line distance in kilometres.
Show the worked solution
- 1 cm represents 50 000 cm = 0.5 km.
- Multiply the measured length: 7.6 × 0.5 = 3.8 km.
- Check that several map centimetres correspond to several kilometres at this scale.
Answer 3.8 km.
From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A plan uses 1 cm for 3 m. What does a 4.2 cm wall represent?
Give me a hint
Multiply the diagram length by the metres per centimetre.
Compare my reasoning
- Each centimetre represents three metres.
- The real length is 4.2 × 3 = 12.6 m.
- State metres, which are the real units in the statement scale.
12.6 m.
Look for these in your work
- Used the diagram-to-real direction.
- Retained the correct units.
Draw a 15 m by 9 m garden at scale 1 : 300. State the diagram dimensions.
Give me a hint
Convert metres into centimetres before dividing by 300.
Compare my reasoning
- The real lengths are 1500 cm and 900 cm.
- Divide each by 300 to obtain 5 cm and 3 cm.
- Use a ruler for a 5 by 3 cm rectangle and label scale 1 : 300.
5 cm by 3 cm.
Look for these in your work
- Converted both dimensions consistently.
- Drew accurate straight edges on paper.
A walk follows two map segments of 3.4 cm and 2.8 cm at 1 : 25 000. Find the total walking distance in kilometres.
Give me a hint
Add the route lengths; do not use the direct distance between endpoints.
Compare my reasoning
- The route totals 3.4 + 2.8 = 6.2 cm.
- One map centimetre represents 25 000 cm = 0.25 km.
- The total is 6.2 × 0.25 = 1.55 km.
1.55 km.
Look for these in your work
- Measured the specified route.
- Converted the ratio scale into kilometres correctly.
Common mistakes
- Mixing metres and centimetres in a ratio scale.
- Multiplying when converting real length to diagram length.
- Measuring a resized onscreen diagram as though it were printed at the stated scale.
What can you explain now?
At 1 : 1000, what real distance does 2 cm represent?
Compare with the explanation
20 m
2 × 1000 = 2000 cm, which is twenty metres.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Tomorrow, choose a room dimension and draw it at two scales. Recover the real length from each drawing to check consistency.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.
Original StudyForA teaching content · AI-assisted checks · Human teacher review pending.
Number contains 19 sequenced lessons; Algebra and graphs 21; Coordinate geometry 10; Geometry 15; Mensuration 13; Trigonometry 13; Transformations and vectors 11; Probability 7; Statistics 13. All 72 syllabus section entries now link to teaching and staged practice. Seven mixed checkpoints sample skills and suggest review lessons. Nine earlier overviews remain available. Full cumulative assessment and human teacher review remain pending. Written lesson practice, charts and constructions are self-checked, not automatically graded. Checkpoints do not save an exam grade or certify mastery.
Check the official syllabus 2025–2027 Open related practice and resources