Question

The area of a quadrilateral ABCD where A = $(0,4,1),B=(2,3,–1),C=(4,5,0)$ and $D=(2,6,2)$ is equal to :

• A. 9 sq. units
• B. 18 sq. units
• C. 27 sq. units
• D. 81 sq. units

Answer 1

The correct option is A 9 sq. units

$\overline{AC}=(4,1,-1),\overline{BD}=(0,3,3)\therefore cos\theta =\frac{0+3-3}{\sqrt{18}\sqrt{18}}=0\Rightarrow sin\theta =1$
Area of quadrilateral ABCD $=\frac{1}{2}|\overline{AC}\times \overline{BD}|=\frac{1}{2}\left(18\right)=9sq.units$