Wiki does try. I skipped over the deduction and looked at the form.

My concern is that it all equates to the difference between two very large numbers, and that coupled with iffy coordinates from an indifferent map, manually chosen............................

Accuracy is somewhat suspect. But better than my first algorithm which needed a centre coordinate and used the Hero's Formula for each triangle clockwise from that point. Which doesn't cope with concave sections.

(I hadn't heard of Hero's or Shoelace Formlae until now)