# Area and distance

How to measure distance on a map using a linear scale. The video also demonstrates how to use grids to estimate the area of a place or feature on a topographic map.

This video:

• details how to measure distance on a topographic map using a linear scale
• demonstrates straight line measurements and strategies to measure distance along a curved route
• details an example of estimating the area of a place or feature.

Watch 'Area and distance' (3:22).

Using linear scale and grids

### Transcript of Area and distance

[Music playing]

[Screen shows a blue sky with clouds. Text on the screen reads, ‘Curriculum Secondary Learners – HSIE. Area and distance. Presented by Melissa Ellis’.]

## Melissa Ellis

If you’re working in Google Maps, you can turn on the distance measurement tool and the distance can be calculated for you.

[Screen shows a street map of Byron Bay from Google Maps. The presenter clicks on the ‘Measure distances and areas’ button in the top left-hand corner of the screen. The button looks like a small grey ruler. The presenter uses the tool to draw dotted lines that measure the length of the beach on the map. The distance between these points automatically calculates itself. It shows that the beach is 1.53km long. Text on screen reads, ‘Google Maps: My Maps, https://www.google.com.au/maps/about/mymaps/, accessed 31 March 2022’.]

There are, however, many different types of maps that geographers use, so you need to know how to do this manually.

[Screen shows a ruler and a hand-drawn topographic map. The map has 5 contour lines. The lines have the heights 10, 20, 30, 40 and 50 written on them. On the 10 line, the presenter has drawn 2 dots. One of the dots is on the west-most part of the line. It is labelled, ‘A’. The other dot is on the east-most part of the line. It is labelled, ‘B’. At the top of the page, the presenter has drawn a compass. The compass is pointing upwards towards the north. Underneath the compass, they have written, ‘contour interval 10m’. At the bottom of the page, the presenter has drawn a scale. The scale reads, ‘2cm:1km’.]

The first measurement is a straight line, or as the crow flies, distance measurement. This is easy to calculate.

[Presenter lines up the ruler so that it connects point A and point B. They place the part of the ruler that reads ‘0mm’ at point A. Point A and point B are 160mm apart.]

Take a piece of paper with a straight edge or a ruler or divider and measure the distance.

[Presenter lines up the ruler with the scale at the bottom of the page. Using the scale, they work out that the real distance would be 8km. Presenter writes, ‘A to B. 8km.’]

Then place this against the linear scale of the map and determine the distance.

[Screen shows the hand-drawn topographic map. This time, the presenter has drawn a small house near the east-most part of the 30 line. They have also drawn a curved and dotted line between point A and the small house. Underneath the last measurement, the presenter has written ‘A to Hut’.]

As we can see from the image, not every distance we need to measure on a map is a straight line. For example, we may want to measure the curved lines around the river or road or land border.

[Presenter places a blank piece of paper along the dotted line. The corner of the paper lines up with point A, and the straight side of the paper lines up with the first part of the dotted line. Every time the dotted line starts to curve, the presenter makes a little marking on the piece of paper. They then shift the paper so that it continues to line up with the dotted line. The presenter repeats this process until the entire length of the dotted line has been marked and measured.]

One simple way to do this is to divide the curve into straight sections and then mark each measurement on a straight-edged piece of paper.

[Presenter lines up the piece of paper with the scale at the bottom of the page. Using the scale, they work out that the real distance would be 6.5km. The final measurement at the bottom of the page now reads, ‘A to Hut. 6.5km’.]

The final measurement can then be converted to an actual distance using the linear scale.

[Presenter removes the piece of paper. They use the cord of their lapel microphone like a piece of string, and they line up the cord with the dotted line. Whenever the dotted line curves, they also curve the microphone cord. They measure the length of the dotted line in this way and then pinch the part of the cord that lines up with the house. The presenter straightens out the cord and brings it down to the scale at the bottom of the page. Using the scale, they once again work out that the real distance would be 6.5 kilometres.]

Another way this can be done is to place a string along the line distance to be measured and then convert this to actual distance using the linear scale.

[Screen shows a piece of grid paper and a ruler. On the grid paper, the presenter has drawn a simple map of a piece of land. The piece of land is an irregular shape. It has a length of 3 grid squares and a breadth of 2 grid squares. The piece of land sits inside a larger rectangle. This rectangle has a length of 6 grid squares and a breadth of 5 grid squares. Above the rectangle, a small scale has been drawn. The scale is 5 grid squares long. On the right-hand side of the page, the presenter has written, ‘Area of one full grid square = 1 x 1 = 1m2’.]

To calculate the area, we first work out the area. A equals length times the breadth of one grid square.

[Presenter points to one of the grid squares on the map. They then point to the formula on the right-hand side of the page.]

In our example, the length and breadth are both one metre.

[Presenter again points to one of the grid squares on the map.]

So the area is one metre squared.

[Presenter points to the piece of land.]

We then multiply this area by the number of grid squares that the feature covers. This will include whole and partial grid squares. To get this number, we first count the whole grid squares and tick these.

[Presenter draws a tick in all of the full grid squares on the piece of land. They tick 3 squares in total.]

Then estimate the partially covered areas.

[Presenter writes the fraction, ‘one-quarter’, in one of the grid squares on the piece of land. They then write the fraction, ‘one-half’, in the 2 remaining grid squares.]

We have 3 whole grid squares and 1.25 partial grid squares.

[Underneath the previous formula, presenter writes, ‘3 + one-half + one-half + one-quarter = 4 and one-quarter’.]

This means that we have a total of 4.25 grid squares.

[Underneath the previous formula, the presenter writes, ‘Area of feature. 1 x 4 and one-quarter = 4 and one-quarter = 4.25m2.]

We then multiply 4.25 by the area of one grid square. Our total area is 4.25 metres squared.

There you have it, measuring distance and area on maps.