Maps and Scale Drawings

Skill 2: Calculating Distances by Measurement

Example: Below is a scale drawing of a portion of coastline. A boat sets off from point A and travels in a straight line to point B. Work out the distance covered by the boat.

The key, shown in the top right, is telling us that every centimetre on the map represents $2$ km in real-life. So, we must firstly measure the distance between A and B on the picture.

It’s important to measure as carefully as you can, because measuring with a ruler is relatively simple, so you will be deducted marks if you’re slightly out.

In this case, we see that the distance is $6.7$ cm. Since the key tells us that each cm is $2$ km, we get the real-life distance travelled by the boat to be:

$6.7 times 2 = 13.4text{ km}$

Skill 3: Calculating Distances using a Grid

Sometimes scale drawings and maps are given using a grid. If the key is given in terms of the numbers of squares on the grid, we don’t need to use a ruler to work out real life distances.

Example: Below is a map of Australia and New Zealand. Calculate the real-life distance between the cities, Melbourne and Auckland, marked on the map.

Here, we can use the scale given in the map:

A distance of two squares is equal to $1000 text{ km}$

We can calculate the distance represented by one square by dividing by $2$:

$begin{aligned}2 text{ squares} &= 1000text{ km} 1text{ square} &=  500 text{ km}end{aligned}$

Next, count the number of squares between the two cities on the map:

There are $5$ squares between Melbourne and Auckland on the map.

Finally, multiply the number of squares by the distance represented by one square on the map to calculate the actual distance between the two cities:

$5times500 text{ km} = 2500 text{ km}$

Skill 4: Calculating the Scale of a Diagram

In some instances, you may be asked to calculate the scale of a diagram if you are given the real-life dimensions. You should try to put your scale into the form “$1$ cm $=$ …”

Example: The diagram below shows a scale drawing of a house that is $10$ m wide.

Calculate the scale of the diagram.

We are told that the width of the house is $10$ m

In the diagram, the house is $5$ cm (five squares) wide.

The scale is therefore:

$5$ cm $=10$ m

Dividing by $5$ gives the answer in the correct form:

$1$ cm $= 2$ m