Assuming the plane is z=0 (otherwise you should so a solid coordinates transformation to bring to this assumption)
You have to loop on the (triangular) faces and search for face that have 3 vertices with z change sign.
For those faces, pick the 2 edges (it must have 2) that have 2 vetices (x1,y1,z1) and (x2,y2,z2) with changing sign of z.
The intersection to the plane z=0 is :
(x,y) = ((x1,y1)*z2 - (x2,2)*z1)/(z2-z1)
Form a graph that links (x,y), you should get a polygon in 2D. Use polyarea to find the area.
