How to calculate area of membrane formed by ring or loop of discrete points?

Question

Given a small set of points (ie 6 to 10) with known xyz coordinates, where this set forms a non-planar closed loop or path, is there a way to numerically calculate the area of a membrane formed by this loop? (ie if this loop were placed in soapy water and then removed, there would be a soap membrane formed that would have a some-what complex 3-D surface, I'm guessing it would be a surface of minimum area or minimum surface tension). Currently I calculate a sort of "plane of best fit" from the points and then project the points onto the plane and then consider this a 2-D area calculation, but I'm curious if there is a way to look at this area as a 3-D membrane.