To get the surface area you need to first determine the surface normal for each point in your mesh of x-y points, as you would to use 'surf'. Use 'meshgrid' to convert your vectors to 2D matrices. Then use 'surfnorm' to determine the surface normal vectors. Next, normalize that normal vector and then use the reciprocal of its z component as the integrand of a numerical double integral taken over your x-y area. This reciprocal is the secant of the angle the normal makes with the z-axis which is the needed factor for conversion from horizontal area to your surface's area.
[X,Y] = meshgrid(x,y);
% Get the corresponding Z values for each pair in X and Y
[Nx,Ny,Nz] = surfnorm(X,Y,Z);
S = sqrt(Nx.^2+Ny.^2+Nz.^2)./Nz; % Secant of angle normal makes with z-axis
% Now S is to be your integrand in the double integral
For this last you can use 'trapz' twice for this purpose, as explained in Walter's reference to my part of Newsreader thread 308496.
