Question

Find the area of the quadrilateral the coordinates of which taken in order, are $(-1,6),(-3,-9),(5,-8)$ and $(3,9)$.

• A. $84$ sq. units
• B. $94$ sq. units
• C. $96$ sq. units
• D. $100$ sq. units

Answer 1

The correct option is C $96$ sq. units

Let $(x_1,y_1)=(-1,6),(x_2,y_2)=(-3,-9),(x_3,y_3)=(5,-8)$ and $(x_4,y_4)=(3,9)$.

Area of the quadrilateral is given by

$\frac{1}{2}\times \left|\begin{array}{ccccc}{x}_1& x_2& x_3& x_4& x_1\\ y_1& y_2& y_3& y_4& y_1\end{array}\right|$

$=\frac{1}{2}\times \left|\begin{array}{ccccc}-1& -3& 5& 3& -1\\ 6& -9& -8& 9& 6\end{array}\right|$

$=\frac{1}{2}\times \left(\right(-1)\times (-9)+(-3)\times (-8)+5\times 9+3\times 6-6\times (-3)-(-9)\times 5-(-8)\times 3-9\times (-1\left)\right)$

$=\frac{1}{2}\times (9+24+45+18+18+45+24+9)$

$=\frac{1}{2}\times \left(192\right)$

$=96$ sq unit