|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| − | 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
| + | #REDIRECT [[Shoelace Theorem]] |
| − | 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
| |
