Coordinate System and Coordinates
8.0 Area of quadrilateral
8.0 Area of quadrilateral
It can be found out by dividing the quadrilateral into two triangles and separately calculating and adding the area of both the triangles using the formulae given in above topic of area of triangle.
\[\begin{gathered}\therefore {\text{ Area of quadrilateral }}ABCD{\text{ = Area of }}\Delta {\text{ABC + Area of }}\Delta {\text{DAC}} \hspace{1em} \\{\text{ = }}\frac{1}{2}\left| {\begin{array}{c}{{x_1}}&{{y_1}}&1 \\ {{x_2}}&{{y_2}}&1 \\{{x_3}}&{{y_3}}&1\end{array}} \right| + \frac{1}{2}\left| {\begin{array}{c}{{x_1}}&{{y_1}}&1 \\ {{x_3}}&{{y_3}}&1 \\ {{x_4}}&{{y_4}}&1 \end{array}} \right| \hspace{1em} \\ \end{gathered} \]
Note: The expression \[\left| {\begin{array}{c}{{x_1}}&{{y_1}}&1 \\{{x_2}}&{{y_2}}&1 \\{{x_3}}&{{y_3}}&1\end{array}} \right|\] can be written in determinant form as \[\left| {\begin{array}{c}{{x_1}}&{{y_1}} \\{{x_2}}&{{y_2}}\end{array}} \right| + \left| {\begin{array}{c}{{x_2}}&{{y_2}} \\{{x_3}}&{{y_3}}\end{array}} \right| + \left| {\begin{array}{c}{{x_3}}&{{y_3}} \\{{x_1}}&{{y_1}}\end{array}} \right|\]
