This question was cross posted on the mathhelpforum and resolved there:
http://www.mathhelpforum.com/math-help/f57/double-application-stokes-theorem-find-area-simplex-167156.html
Of course, if someone has a different explanation, it's welcome.
I'm having trouble using Stokes' theorem in order to find a simple formula for the area found within a two dimensional simplex. I know the formula, but I'm interested in the derivation. For simplicity, I've been working with a unit triangle with vertices at the coordinates (0,0), (0,1), and...