When a map shrinks every length by the same factor, it shrinks area by that factor squared. To find a real area, convert the length and width to real distances and multiply those, or multiply the map area by the square of the scale. It appears when you estimate the size of a lake, a built-up area or a field from a map.
This lesson builds on converting a map distance within scale, distance and relief.
Why does area change faster than length?
Take a map square of 1 cm by 1 cm on a 1:50 000 map. Each side is 500 m on the ground. The real square is 500 m × 500 m = 250 000 m².
The length scale is 1 to 50 000, but the area scale is 1 to 50 000², which is 1 to 2 500 000 000. That is why 1 cm² on the map is 250 000 m², or 0.25 km².
How do you find a real area, step by step?
- Convert each map length to a real length in km (or m) using the scale.
- Multiply the two real lengths to get the area, keeping the unit squared.
- Or use the fact for 1 cm² on that map, and multiply by the map area in cm².
- Write the unit as km² or m², not km or m.
Worked example
The numbers here are invented for practice. On a 1:50 000 map, a rectangular reservoir measures 3 cm by 2 cm. Find its real area in km².
Method 1, convert lengths: 3 cm × 500 m = 1 500 m = 1.5 km. 2 cm × 500 m = 1 000 m = 1 km. Area = 1.5 × 1 = 1.5 km².
Method 2, use the 1 cm² fact: the map area is 3 × 2 = 6 cm². Each cm² is 0.25 km², so 6 × 0.25 = 1.5 km².
Both methods agree. Method 1 is easier to defend if a step is questioned.
The mistake to watch for
Mistaken answer: map area = 6 cm², and 6 × 0.5 km = 3 km².
The student used the length scale (1 cm is 0.5 km) on an area.
The answer of 3 km² is twice the correct 1.5 km². The slip happens because the length fact is easy to remember and the area fact is not.
To correct it, ask: “Did I convert two lengths, or one area?” If you convert an area, you need the square of the length conversion.
Check yourself
1. On a 1:25 000 map, what real area does 1 cm² represent, in km²?
Show answer
1 cm is 250 m. A 250 m by 250 m square is 62 500 m², which is 0.0625 km².
2. A wood measures 4 cm by 5 cm on a 1:25 000 map. Find its real area in km².
Show answer
4 cm is 1 km and 5 cm is 1.25 km. Area = 1 × 1.25 = 1.25 km². Check: 20 cm² × 0.0625 = 1.25.
3. A farm covers 6 km². On a 1:50 000 map, what area in cm² does it cover?
Show answer
Each cm² is 0.25 km², so 6 ÷ 0.25 = 24 cm². Check: a 3 km by 2 km farm is 6 cm by 4 cm, and 6 × 4 = 24.
Where this leads next
Return to map distance conversion if lengths still feel shaky, or move on to reading contours and relative height. The map scale, contour and gradient practice tool has area conversions to rehearse.
The square idea is easier to hold when someone draws it with you, and a teacher in online one-to-one Geography tuition can do that at your pace.