Conversion of $2\:\text{m}^2$ in $\text{cm}^2$

Question

I had an evaluation and had to go from $2\:\text{m}^2$ to $\text{cm}^2$ and I made a rule of three simple: $1\:\text{m}^2 = 10000\:\text{cm}^2,$ $2\:\text{m}^2 = 20000\:\text{cm}^2.$ But the teacher told me wrong, he told me it was like this: $1\:\text{m}^2 = 100\times 100.$ $2\:\text{m}^2 = 200\times 200 = 40000\:\text{cm}^2.$ I think it's wrong and if so, tell me why, in order to explain it to me and that it's correct. Thank you.

Answer 1

Yes of course we have

• $1\,m^2 =100\times 100 \,cm^2 = 10'000 \,cm^2 \implies 2\,m^2 =20'000 \,cm^2$

and

• $2\,m\times 2\,m = 4 \, m^2= 40'000 \,cm^2$

Answer 2

Your teacher is wrong since $100*100*2\neq 200*200$. This is because on the RHS there are two factors of $2$ whereas there is only $1$ factor of a $2$ on the LHS.

Answer 3

We have $$1\:\text{m}=100\:\text{cm}$$ so $$1\:\text{m}^2=100\cdot 100\:\text{cm}^2=10000\:\text{cm}^2$$ so $$2\:\text{m}^2=2\cdot 10000\:\text{cm}^2=20000\:\text{cm}^2.$$

Answer 4

There is possibly some ambiguity over two metres squared

• An area of $2$ square metres is the same as an area of $20000$ square centimetres, for the reason you give

• A square with a side of $2$ metres has an area of $2^2=4$ square metres; in the same way a square with side $200$ centimetres has an area of $200^2=40000$ square centimetres

Answer 5

Let's imagine a square with side measurements of $1m$. Its area is $1m*1m=1m^2$

Now, $100cm=1m$. If we imagine a square with side lengths $100cm$, it's area is $100cm*100cm=10000cm$.

Imagine a square with sides $2m$. It's area is $4m^2$.

With sides of $200cm$, we get an area of $200cm^2=40000cm^2$

And so on and so forth. Basically, you're completely correct, $1m^2=10000cm^2$.