9.0 Area of $n$- sided polygon

Area of polygon formed by the points $({x_1},{y_1}),{\text{ }}({x_2},{y_2}),{\text{ }}({x_3},{y_3}),...................({x_n},{y_n})$ is given by

\[\frac{1}{2}(\left| {\begin{array}{c}{{x_1}}&{{y_1}} \\ {{x_2}}&{{y_2}} \end{array}} \right| + \left| {\begin{array}{c}{{x_2}}&{{y_2}} \\ {{x_3}}&{{y_3}} \end{array}} \right| + ................. + \left| {\begin{array}{c}{{x_{n - 1}}}&{{y_{n - 1}}} \\ {{x_n}}&{{y_n}} \end{array}} \right| + \left| {\begin{array}{c}{{x_n}}&{{y_n}} \\ {{x_1}}&{{y_1}} \end{array}} \right|)\]

Note: $n$-sided polygon can be considered as the sum of area of $\frac{n}{2}$ triangles.