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Mathematik-Online problems:

Problem 231: Area of a General Polygon

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Show that the area of a plane polygon with n vertices, $ Q_1,\,\ldots,\, Q_n$, can be calculated by the formula

$\displaystyle A=\frac{1}{2}\left\vert \sum_{i=1}^{n}\left(\overrightarrow{Q_{i-... ... \times \overrightarrow{Q_{i-1}P\,}\right) \, \right\vert\,, \qquad Q_0=Q_n, $

where $ P$ is an arbitrary point.

Solution:

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  automatisch erstellt am 6.  2. 2018