Area of the region of the complex plane enclosed between two paths

Question

Suppose ${\cal U}\subset\mathbb C$ is a complex domain and $\gamma_0,\gamma_1 : [0,1]\to {\cal U}$ are two piecewise $\mathscr C^1$ paths, sharing the same start and end points, i.e. $\gamma_1(0)=\gamma_0(0), \gamma_1(1)=\gamma_0(1)$. Is there a way to compute the area of the region enclosed between $\gamma_0$ and $\gamma_1$?