Convert square units and hectares using area factors
Square a length conversion factor for area · Use hectares and square kilometres · Check that an area conversion cannot use the linear factor
Section Paper 2 · Historical Extended · non-calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Metric lengths
- Rectangular area
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Square a length conversion factor for area
- Use hectares and square kilometres
- Check that an area conversion cannot use the linear factor
Convert both dimensions
Since 1 cm = 10 mm, a 1 cm by 1 cm square is 10 mm by 10 mm, so 1 cm² = 100 mm². Similarly, 1 m² = 10 000 cm² and 1 km² = 1 000 000 m². Square the length factor; do not multiply by it only once.
The diagram partitions a 1 m square into 100 tiles, each 10 cm by 10 cm. Each tile has area 100 cm², giving 10 000 cm² in total. It does not show 100 one-centimetre tiles.
Land area
1 hectare (ha) = 10 000 m². Since 1 km² = 1 000 000 m², 1 km² = 100 ha. To convert from m² to ha, divide by 10 000; to convert from ha to km², divide by 100. Area is measured in square units even when a land unit has a special name.
Sources for this lesson
Pause and explain
What is 1 m² in cm²?
Worked example
Convert 2.4 m² to cm².
Show the worked solution
- Each metre dimension contributes a factor of 100.
- 2.4×100² = 24 000 cm².
Answer 24 000 cm².
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →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.
Convert 3 cm² to mm².
Give me a hint
Square the factor of 10.
Compare my reasoning
- 1 cm² = 100 mm².
- 3×100 = 300 mm².
300 mm².
Look for these in your work
- Use a squared factor
- Keep square units
Convert 0.06 km² to hectares and square metres.
Give me a hint
Use 100 ha and 1 000 000 m² per km².
Compare my reasoning
- 0.06×100 = 6 ha.
- 0.06×1 000 000 = 60 000 m².
6 ha; 60 000 m².
Look for these in your work
- Use the correct land factors
- Cross-check the two answers
A 250 m by 80 m field is advertised as 2 hectares. Verify the claim.
Give me a hint
Calculate its area in m² before converting.
Compare my reasoning
- Area = 250×80 = 20 000 m².
- 20 000÷10 000 = 2 ha.
Yes: 20 000 m² = 2 ha.
Look for these in your work
- Use both dimensions
- Compare in one unit
Common mistakes
- An area factor is the square of the length factor.
- One hectare is 10 000 m², not 100 m².
What can you explain now?
What is 1 m² in cm²?
Compare with the explanation
10 000 cm².
Both sides of the unit square become 100 cm.
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Make it stick
What is 1 m² in cm²?
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.