Experimath - Experiment 3

Syllabus links

Key Stage 2 (age 7 to 11)

How much land is there in the United Kingdom? Use triangles to find out!

This experiment gives children an opportunity to use the formula for calculating the area of a triangle in a realistic situation.

The child will learn that estimates and approximations can be more accurate the more parts they are broken down into.

how to calculate the area of a triangle (half the base times the height [at right angles to the base])

a printer

a pencil

a ruler

Right-click the image to save it.

Open the map in your graphics program (you can probably just double-click it in the folder where you downloaded it).
Print at least three copies of it, as large as you can.
On your first printed map, draw one large triangle over the main island (Great Britain), covering it as closely as possible.
Calculate the area of this triangle in square centimetres.

Write this area on the map.
Use the scale on the map to convert this area to square kilometres.

Write this area on the map.
Repeat this on your second map, but this time use about five triangles. Include Northern Ireland.
Repeat this again. Use as many triangles as you feel you need in order to get a good approximation.

The CIA World Factbook, which was the source of this image, gives the land area of the UK as 241,930 km².
If you use more triangles, your approximation can more closely fill the land without any of the water. This should lead to a more accurate estimate.

However, if you use too many triangles there will be lots of small ones, which could be difficult to measure accurately.

Use this approach on copies of some other maps to calculate the area of other countries.

Country maps are available from Wikipedia or the CIA World Factbook.

Experiment 3 v4