non-orthogonal area

George

Hello, I am writing a 3D finite volume code in curvilinear coodinates and I have one important question. In cartesian coordinates, the area (for example at the z-axis AREA(z)=dx.dy), where dx=x(i,j,j)-x(i-1,j,k) and it is ALWAYS positive. At the curvilinear coordinates now, there is again the area, and it is given in a similar way than that in cartesian corodinates (AREA(z)=dx1.dy1+dx2.dy2+dx3.dy3), where dx1,dy1, etc are the distances along the axis in every direction. There is the possibility here this area not to be positive. My question is that we should take the ABSOLUTE value of this area, or leave it with its algebraic symbol(+ or -).

Thank you for reading my question and I would like a quick response (if possible), because it is quite urgent.