# How do we define "area" and "volume" dimensionally?

Well, $\text{area "=" length"xx"breadth}$.
And $\text{volume" = "length"xx"breadth"xx"height}$
Note that this treatment is consistent dimensionally. $\text{Area}$ has units of ${m}^{2}$, given the above formula. And of course, the units of $\text{volume}$ $=$ $m \times m \times m$ $=$ ${m}^{3}$.