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 m ^{2} = 100 cm^{2}**.

BUT, in reality, **1 m ^{2} = 10000 cm^{2}** 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 m^{2} = 10000 cm^{2}

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 m ^{2} into cm^{2}.**

We know that for length, 1 m = 100 cm.

So for area, 1 m^{2} = 10000 cm^{2}.

So 1.4 m^{2} = 1.4 × 10000 = 14000 cm^{2}.

**e.g. Convert 350 m ^{2} into km^{2}.**

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

So for area, 1 km^{2} = 1000000 m^{2}.

So 350 m^{2} = 350 ÷ 1000000 = 0.00035 m^{2}.

In this activity, we will convert areas (expressed in cm^{2}, m^{2} and km^{2}) into alternative units of measurement by applying the area conversion factor using the methods shown above.