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Shoestring: Difference between revisions

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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) ...  
You stack them vertically until you reach the first vertex make sure you list 1st vertex again at the bottom.
For a quadrilateral, this step would look like


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.


E F
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:


G H
2 1=2  0 1=0


A B
1 3=3  2 3=6


Now you find cross products. First all the diaonally down to the left. This would mean BC, DE, FG, and HA. Then these are added.
0 2=0  2 2=4
Then diagonally to the right. This would mean AD, CF, EH, and GB. These are also added.
 
the area is half of the positive difference between the sums
2 0=0  1 0=0
 
  =5    =10
 
area is 2.5

Revision as of 20:45, 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

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