Rates, ratios & proportions · Ages 13–14
Scales on maps and plans
Lengths times the scale; areas times the scale squared.
How to do it
Method
Lengths times the scale; areas times the scale squared
6 × 50000 = 300000 cm = 3 km
Another way
1 cm first
1 cm stands for 500 m: 1 cm² for 500 × 500 = 250000 m²
In full
A map's scale of 1 : 50000 means 1 cm on the map stands for 50000 cm, that is 500 m, on the ground. Real distance = map distance × 50000, then change units: 6 cm on the map is 6 × 50000 = 300000 cm = 3 km. The other way, map distance = real distance ÷ 50000, both in the same unit. Areas are different: the length and the width are both 50000 times as big, so the area is 500002 times as big. One way, the ratio of areas first: 1 : 500002 = 1 : 2500000000, so 4 cm² on the map is 4 × 2500000000 = 10000000000 cm² = 1 km². Another, turn 1 cm into a real length first: 1 cm stands for 500 m, so 1 cm² stands for 500 m × 500 m = 250000 m², and 4 cm² for 1000000 m² = 1 km². The usual slip with a real area is multiplying by 50000 only once.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
On a plan with scale 1 : 1000, what real length in metres do 7 cm stand for?
- A. 7 m
- B. 700 m
- C. 7000 m
- D. 70 m
Choose the right answer
Show the answer and working
Answer: D. 70 m
Real length = 7 × 1000 = 7000 cm = 70 m.
Example 2
On a map with scale 1 : 2000, a park covers 6.5 cm². What is the park's real area in m²?
Show the answer and working
Answer: 2600 m²
1 cm stands for 20 m, so 1 cm² for 20 × 20 m²: 6.5 × 20 × 20 = 2600 m².
Example 3
A map's scale is 1 : 20000. A rectangular plot is 11 cm by 7 cm on it. What is its real area in km²?
Show the answer and working
Answer: 3.08 km²
1 cm stands for 0.2 km: really 2.2 km by 1.4 km, an area of 2.2 × 1.4 = 3.08 km².
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.A map's scale is 1 : 10000. A real 14 km = cm, which is cm on the map.
Fill in each blank
Answer:
2.A map's scale is 1 : 20000: 11.5 cm on it stand for km
Answer:
3.On a map with scale 1 : 2000, a park covers 15.5 cm². What is the park's real area in m²?
Answer:
4.The same area of land is drawn on a map with scale 1 : 20000, then on one with scale 1 : 2000. How many times its area on the first map is its area on the second?
- A. 10 times
- B. 20 times
- C. 100 times
- D. 0.01 times
Choose the right answer
Answer:
5.A map's scale is 1 : 50000. A rectangular plot is 5 cm by 2 cm on it. What is its real area in km²?
Answer:
All the answers
- 1. 1400000, 140
- 2. 2.3
- 3. 6200 m²
- 4. C. 100 times
- 5. 2.5 km²
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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