If lengths scale by k, areas scale by k² — including map areas.
Key formulas
Length first
Scale 1:20000 means 1 cm on the map is 20000 cm = 200 m in reality.
Area
A field that is 3 cm² on the map has real area 3 × (20000)² cm². Convert systematically to m² or km².
Trap
Students scale area by 20000 instead of 20000². That underestimates massively.
Worked example
Worked example
Problem. Scale 1 : 10000. A park is 2 cm² on the map. Find the real area in m².
Solution. Length factor k = 10000. Area factor = k² = 10⁸. Real area = 2 × 10⁸ cm² = 2 × 10⁸ / 10⁴ = 20000 m².
Square check
A 1 cm × 1 cm map square → side 200 m → area 40000 m².
Review quiz
Scale 1:20000. 1 cm² on the map is how many m² in reality?
Practice questions
- Scale 1:10000. Map area 2 cm². Find real area in m².
- Why is the area factor the square of the length factor?
Study notes
Volume on maps?
Maps are 2D; volume needs a height from elsewhere.
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