Question

Find the area of the quadrilateral $ABCD$ whose vertices are $A(-4,-2),B(-3,-5),C(3,-2),D(2,3)$.

Answer 1

Area of quadrilateral $ABCD=$Area of $△ABC+$Area of $△BCD$

$=\frac{1}{2}\left|\begin{array}{ccc}-4& -2& 1\\ -3& -5& 1\\ 3& -2& 1\end{array}\right|+\frac{1}{2}\left|\begin{array}{ccc}-3& -5& 1\\ 3& -2& 1\\ 2& 3& 1\end{array}\right|=\frac{21}{2}+\frac{35}{2}=28$