Question

How do I find the area of a polygon with given vertices?

Answer 1

1.Make a table with the x,y coordinates of each vertex. Start at any vertex and go around the polygon in either direction. Add the starting vertex again at the end. You should get a table that looks like the leftmost gray box in the figure above.
2.Combine the first two rows by:
Multiplying the first row x by the second row y. (red)
Multiplying the first row y by the second row x (blue)
Subtract the second product form the first.
3.Repeat this for rows 2 and 3, then rows 3 and 4 and so on.
4.Add these results, make it positive if required, and divide by two.

It’s really simple if you think about it