Sally, do you know the points of the vertices (corners) of your polygon? Are you trying to do this for the shading and lighting for 3d graphics? If you know the points of the vertices then calculating the normals is a piece of cake. The only thing you need to consider is which way is "up" on your polygon. I assume you want each of the normals pointing in the same direction.

That said, I'm still confused about what exactly you are after. Perhaps it would help if you could tell us why you are trying to get the information?

I took a look at what you wrote about finding equations for the line segments that make up a polygon. You don't need normals to the line segments to use in your calculation, just the points in space for each vertex of your polygon.

As far as I know the cross product is only defined for 3D or 7D. 2D is just 3D with one of the other components zero.