Pullback of area form of manifold by local chart map

Question

Let $M$ be an orientable $2$-manifold in $\mathbb{R}^n$, with area form $dA$. Let $\phi: U \to M$ be a local coordinate system for $M$, with $U \subseteq \mathbb{R}_{uv}^2$. It is stated that $\phi^*(dA) = (EG-F^2)^\frac{1}{2} dudv$, where $E, G, F$ are the coefficients of the first fundamental form. Why is that so?