Shoestring

This formula finds the area of any 2-D figure whose coordinates of the vertices are known and the order in which the vertices are connected given coordinates (in order) (A,B) (C,D) ...

One method is to list the x coordinates in order vertically and then move the first coordinate to the bottom. List the y coordinates in order next to the x coordinates. To the right a little, list the x coordinates in order and then move the last coordinate to the top. Next to the 2nd x coordinate list, again list the y coordinates in order.

Multiply the lists horizontally *only the 2 right lists together and the 2 left lists together* , add vertically, find half the positive difference between the 2 sums. for a quadrilateral with vertices (2,1) (2,3) (1,2) and (0,0) this means:

2 1=2 0 1=0

1 3=3 2 3=6

0 2=0 2 2=4

2 0=0 1 0=0

  =5     =10

area is 2.5