
This is something that many people get wrong.
There are 100 centimetres in 1 metre. But this does not mean that there are 100 square centimetres in a square metre!
Think of a frame measuring 1 square metre. Start filling it with small square counters which are 1 square cm. You will fit 100 of them along the bottom row, then 100 along the next row, and so on. Overall, (up the side) there will be room for 100 rows.
So overall, the square metre contains 100 rows each of 100 square centimetres. Therefore
1 square metre = 100 × 100 = 10000 square centimetres
A handy way to remember this:
If the scale factor between the basic units (here, m and cm) is 100, then the scale factor
between the squared units is 100 squared which is 10000