area of polygon

Let the vertices of a () polygon be $(x_{1},\,y_{1}),\,(x_{2},\,y_{2}),\,\ldots,\,(x_{n},\,y_{n})$ , enumerated in when gone round the polygon anticlockwise. The area of the polygon is equal to

$\frac{1}{2}\left(\left|\begin{matrix}x_{1}&x_{2}\\ y_{1}&y_{2}\end{matrix}\right|+\left|\begin{matrix}x_{2}&x_{3}\\ y_{2}&y_{3}\end{matrix}\right|+\ldots+\left|\begin{matrix}x_{n-1}&x_{n}\\ y_{n-1}&y_{n}\end{matrix}\right|+\left|\begin{matrix}x_{n}&x_{1}\\ y_{n}&y_{1}\end{matrix}\right|\right).$

References

1 E. Lindelöf: Johdatus korkeampaan analyysiin. Neljäs painos. Werner Söderström Osakeyhtiö, Porvoo and Helsinki (1956).

Title	area of polygon
Canonical name	AreaOfPolygon
Date of creation	2013-03-22 17:32:57
Last modified on	2013-03-22 17:32:57
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	6
Author	pahio (2872)
Entry type	Result
Classification	msc 15A63
Classification	msc 51M25
Related topic	Area
Related topic	Determinant2
Related topic	CentreOfMassOfPolygon