Area of Triangle and Quadrilateral

Things to remember

∴ \(\square\)ABCD = ½\(\begin{vmatrix}x_1&x_2&x_3&x_1\\y_1&y_2&y_3&y_1 \end{vmatrix}\) + ½ \(\begin{vmatrix}x_1&x_3&x_4&x_1\\y_1&y_3&y_4&y_1 \end{vmatrix}\)

=½ (x₁ y₂-x₂ y₁+x₂ y₃-x₃ y₂+x₃ y₁-x₁ y₃) +½ (x₁ y₃-x₃ y₁+x₃ y₄-x₄ y₃+x₄ y₁-x₁ y₄)

=½ (x₁y₂-x₂y₁+x₂y₃-x₃y₂+x₃y₄-x₄y₃+x₄y₁-x₁y₄)

Note : To find the area of a quadrilateral by using this formula, the vertices of quadrilateral should be taken in order. So it is better to plot the points roughty before applying the formula. Otherwise the result may be wrong.   

Note: To find the area of a quadrilateral, we divide it into two triangles by joining a diagonal. Then the sum of the areas of the two triangles will be equal to the area of the quadrilateral.