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How to convert units of length and area

Units for length

$ 1 \text{ m} = \phantom{.} $ $ 100 $$ \text{ cm}$


$ 1 \text{ km} = \phantom{.} $ $ 1000 $$ \text{ m}$

Units for area

$ 1 \text{ m}^2 = \phantom{.} $ $ 100 \times 100 $$ \text{ cm}^2$


$ 1 \text{ km}^2 = \phantom{.} $ $ 1000 \times 1000 $$ \text{ m}^2$

What is a map scale?

A map scale tells us how distances on a map compare to the actual distances in real life.

For example, a scale of $1 : 500 \phantom{.} 000$ means:

\begin{align*} \text{Map} & : \text{Actual} \\ 1 & : 500 \phantom{.} 000 \end{align*}

This means that $1$ unit on the map represents $500 \phantom{.} 000$ of the same unit in real life.

For example, if we use cm, then:

$$ 1 \text{ cm} = 500 \phantom{.} 000 \text{ cm}$$

Since $500 \phantom{.} 000 \text{ cm} = 5 \text{ km}$, we can also say:

$$ 1 \text{ cm} = 5 \text{ km}$$

How to convert between length scale and area scale

Convert length scale to area scale

$ 1 \text{ cm } : 2.5 \text{ km} $

$1^2$ $ \text{ cm}^2 \phantom{.} :$ $ 2.5^2 $$ \text{ km}^2$

Convert area scale to length scale

$ 1 \text{ cm}^2 : 0.25 \text{ km}^2 $

$\sqrt{1}$ $ \text{ cm} \phantom{.} :$ $ \sqrt{0.25} $$ \text{ km}$

Practice questions

Map scale questions involving length and area

1. A map has scale $1 : 20 \phantom{.} 000$.

(a) A canal has length of $6.7$ cm on the map. Find the actual length of the canal in kilometres (km).

Answer: $ 1.34 \text{ km} $

Solutions

(b) A park has actual area of $240 \phantom{.} 000$ m2. Find the area of the park on the map in cm2.

Answer: $ 6 \text{ cm}^2 $

Solutions


2. A shopping mall with actual area of $1.12$ km2 is represented by an area of $0.28$ cm2 on a map. Find the scale of the map in the form $1 : n$.

Answer: $ 1: 200 \phantom{.} 000 $

Solutions

Map scale questions with two maps of different scales

3. Map A has scale of $1:10 \phantom{.} 000$ while Map B has a scale of $1:25 \phantom{.} 000$. A resort that appears on both maps is represented by $5$ cm2 on Map A. Find the area of the resort on Map B in cm2.

Answer: $ 0.8 \text{ cm}^2 $

Solutions

O Level past year questions on map scales

Year & paper Comments
2024 P1 Question 6
2023 P1 Question 1c (numbers are given in standard form)
2020 P1 Question 17
2019 P1 Question 23a (diagram is drawn to scale, i.e. use ruler to measure the length)
2016 P1 Question 20
2012 P1 Question 10
2011 P1 Question 9

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