You may be familiar with converting between different units (e.g. m and cm, or m and km), but how do we apply this when we are also calculating areas? 

When we are converting from, for example, metres into cm, we know that 1 m = 100 cm.

This can lead to the misconception that 1 m² = 100 cm².

BUT, in reality, 1 m² = 10,000 cm² as we need to take into account our area conversion factors. 

Let's look at what we mean here with a diagram to help. 

If we look at a square that measures 1 m on each side:

Looking at the areas of these two identical squares, we can say that:

1 m × 1 m = 100 cm × 100 cm

1 m² = 10,000 cm²

Is there a trick?

In a way, yes.

All we need to do for an area conversion is to find the conversion if it was a length, and then square it to get the area conversion.

Let's look at an example to see this in action.

e.g. Convert 1.4 m² into cm²

We know that for length, 1 m = 100 cm

So for area, 1 m² = 10,000 cm²

So 1.4 m² = 1.4 × 10,000 = 14,000 cm²

e.g. Convert 350 m² into km²

We know that for a length, 1 km = 1000 m

So for area, 1 km² = 1,000,000 m²

So 350 m² = 350 ÷ 1,000,000 = 0.00035 m²

In this activity, we will convert areas (expressed in cm², m² and km²) into alternative units of measurement by applying the area conversion factor using the methods shown above.