Difference between revisions of "Shoelace"
(New page: Let <math>(x_1, y_1)</math>, <math>(x_2, y_2)</math>, <math>(x_3, y_3)</math>,..., <math>(x_n, y_n)</math> be the coordinates of the vertices, arranged counterclockwise, of an n-sided con...) |
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Let <math>(x_1, y_1)</math>, <math>(x_2, y_2)</math>, <math>(x_3, y_3)</math>,..., <math>(x_n, y_n)</math> be the coordinates of the vertices, arranged counterclockwise, of an n-sided convex polygon. Then the area of the polygon is given by the formula | Let <math>(x_1, y_1)</math>, <math>(x_2, y_2)</math>, <math>(x_3, y_3)</math>,..., <math>(x_n, y_n)</math> be the coordinates of the vertices, arranged counterclockwise, of an n-sided convex polygon. Then the area of the polygon is given by the formula | ||
| − | <math>(x_1y_2 + x_2y_3 + x_3y_4 + ... + x_{n-1}y_n+ x_ny_1 - x_2y_1 - x_3y_2 - x_4y_3 - ... x_ny_{n-1}- x_1y_n)/2</math> | + | <math>(x_1y_2 + x_2y_3 + x_3y_4 + ... + x_{n-1}y_n+ x_ny_1 - x_2y_1 - x_3y_2 - x_4y_3 - ... - x_ny_{n-1}- x_1y_n)/2</math> |
Revision as of 06:50, 9 May 2009
Let 
, 
, 
,..., 
be the coordinates of the vertices, arranged counterclockwise, of an n-sided convex polygon. Then the area of the polygon is given by the formula
