Any old time land surveyors out there?

I am looking for the method for calculating the area of an iregular land mass.

I am asking for the oldtimers 'cause back in the eighties, I started to take a survey course, but had to leave before it got too far into it. Just before I had to leave, might even have been the last day, the teacher gave us a method to calculate this type of area using the xy coordinates. Stupid me, I didn`t write down his method or the setup for the coords, just his proof. I was looking through my notes recently (yes I am anal enough to have kept some partial course notes for more than 25 years) and found the proof. For the very life of me, I can not figure out the method, and I really have tried to solve it.


HEEEEELP!!!!!