Area convergence

Question

Let $(M^3,g)$ be a compact, connected and oriented Riemannian manifold with boundary. Let $\{\Sigma_n\}_{n \geq 1}$ be a sequence of free boundary minimal surfaces embedded in $M$ that converges smoothly to a smooth and embedded free boundary minimal surface $\Sigma \subset M$ with multiplicity $k \geq 1$. Can I conclude that the areas converge too? That is, does it hold that $$\operatorname{Area}(\Sigma) = \frac{1}{k} \lim_{n\to \infty} \operatorname{Area}(\Sigma_n)?$$