Difference between revisions of "Shoestring"
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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 | 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) ... | 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 | ||
Revision as of 21:45, 23 April 2008
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
