Question

$A(-5,-3),B(-4,-6),C(2,-1)$ and $D(1,2)$ are the vertices of a quadrilateral $ABCD$. Find the area of the quadrilateral?

Answer 1

Area of the quadrilateral formed by joining the vertices

$(x_1,y_1),(x_2,y_2),(x_3,y_3)$ and $(x_n,y_n)$

is $\frac{1}{2}\Vert \begin{array}{cc}{x}_1-x_3& x_2-x_4\\ y_1-y_3& y_2-y_4\end{array}\Vert =\frac{1}{2}\Vert \begin{array}{cc}-7& -5\\ -2& -8\end{array}\Vert =\frac{1}{2}\left|\right(56-10\left)\right|=23$ sq. unit