# Area of a mesh patch given the corners

I have a mesh $$\mathcal{M}$$ and 4 vertices $$v_1, v_2, v_3, v_4$$, I know the connectivity but not the geometric path. $$\mathcal{M}$$ is a single connected component (with no holes). What's the quickest/easiest way to compute the area delimited from these 4 points?

I don't know the actual geometric path but if $$v_i$$ is connected to $$v_{i+1}$$ I know for sure they're connected by a geodesic path.

Is there like a simple algorithm to commpute the area?

Thank you.