Question

The area (in sq. units) of the quadrilateral whose vertices are $A(1,1),$ $B(3,4),$ $C(5,-2)$ and $D(4,-7)$ is

• A. $41$
• B. $64$
• C. $\frac{37}{4}$
• D. $\frac{41}{2}$

Answer 1

The correct option is D $\frac{41}{2}$

The area of quadrilateral
$=\frac{1}{2}\left|\begin{array}{ccccc}{x}_1& x_2& x_3& x_4& x_1\\ y_1& y_2& y_3& y_4& y_1\end{array}\right|=\frac{1}{2}\left|\begin{array}{ccccc}1& 3& 5& 4& 1\\ 1& 4& -2& -7& 1\end{array}\right|=\frac{1}{2}|(4-3)+(-6-20)+(-35+8)+(4+7)|=\frac{1}{2}|1-26-27+11|=\frac{41}{2}\text{sq. units}$