Question

The area of the quadrilateral $ABCD$ with $A(1,0,)B(5,3),C(2,7)$ and $D(-2,4)$ is

• A. $12sq.units$
• B. $25sq.units$
• C. $20sq.units$
• D. $24sq.units$

Answer 1

The correct option is B $25sq.units$

Let $A(1,0,)B(5,3),C(2,7)$ and $D(-2,4)$ be the vertices of quadrilateral $ABCD$

Area of quadrilaterl $ABCD=\frac{1}{2}[\left|\begin{array}{cc}{x}_1& x_2\\ y_1& y_2\end{array}\right|+\left|\begin{array}{cc}{x}_2& x_3\\ y_3& y_3\end{array}\right|+\left|\begin{array}{cc}{x}_3& x_4\\ y_3& y_4\end{array}\right|+\left|\begin{array}{cc}{x}_4& x_1\\ y_4& y_1\end{array}\right|]$

$=\frac{1}{2}[\left|\begin{array}{cc}1& 5\\ 0& 3\end{array}\right|+\left|\begin{array}{cc}5& 2\\ 3& 7\end{array}\right|+\left|\begin{array}{cc}2& -2\\ 7& 4\end{array}\right|+\left|\begin{array}{cc}-2& 1\\ 4& 0\end{array}\right|]$

$=\frac{1}{2}[(3-0)+(35-6)+(8+14)+(0-4)]$

$=\frac{1}{2}\times 50=25sq.units$