Graph of a continuous function has measure zero

I need help to solve the following problem:

Let $f: \mathbb{R}^n \rightarrow \mathbb{R}$ be a continuous function. Prove that the graph$$G(f)=\{(x,f(x)):x\in\mathbb{R}^n\}$$has measure zero in $\mathbb{R}^{n+1}$.

I suppose that I have to use that $f$ es uniformly continuous, but I don't know what rectangle whose sum of volumes is less than $\varepsilon > 0$ should I take.