005

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Excerpted from notes written on 2017-07-05

(Polygon Area)Given an arbitrary polygon on the coordinate plane formed by \(n\) points, prove that the area of the shape can be expressed in the following form:

\[ {1\over2} \times \left| \left(\sum_{i=0}^{n-1} {x_{i}y_{i+1} - x_{i+1}y_{i}}\right) + (x_{n}y_{1} - x_{1}y_{n}) \right| \]