1. General
Once a loop traverse has been adjusted, how can its area be determined?
Figure G1 Loop Traverse 
We could divide the complex polygon into a series of triangles, compute the area of each triangle, then total them, Figure G2.
Figure G2 
Figure G3 demonstrates that there can be quite a few possible triangle combinations for a five sided traverse.

Figure G3 
To compute a triangle's area, either all three sides or two sides and an included angle are needed. That means additional calulations must be carried out to obtain distanaces and/or an angle between lines. In both triangle combinations of Figure G3, the red lines must be computed by inversing.
The traverse in Figure G3 is a bit simplistic with just five sides. The more traverse points, the more triangles and combinations and more inverse calculations. It can be especially interesting approach with a concave traverse, Figure G4, having one or more situations where triangle areas should be subtracted instead of added.Just ome more thing to keep track of.
Figure G4 
As with other surveying calculations, we need a systematic, repeatable, and reliable approach to determine traverse area.