you might just intersect your plane with the loft and from the (closed) curve(s) create planar surface(s). Below is an example using the WorldXY Plane. Once you have the resulting planar surface, print out the area.
import Rhino
import scriptcontext
import rhinoscriptsyntax as rs
def DoSomething():
id = rs.GetObject("Select surface or polysurface", 8+16, True, False)
if not id: return
tol = scriptcontext.doc.ModelAbsoluteTolerance
brep = rs.coercebrep(id, True)
plane = Rhino.Geometry.Plane.WorldXY
rc, crvs, pts = Rhino.Geometry.Intersect.Intersection.BrepPlane(brep, plane, tol)
if not rc: return
breps = Rhino.Geometry.Brep.CreatePlanarBreps(crvs)
if not breps: return
ids = [scriptcontext.doc.Objects.AddBrep(b) for b in breps if b.IsValid]
if len(ids) != 0:
rs.SelectObjects(ids)
else:
print "No surface(s) built"
if __name__=="__main__":
DoSomething()
To move the plane around, just change it`s origin.