Answer
$=\sqrt {269}$ units
Work Step by Step
Area of a parallelogram with vertices $PQRS$ is defined as:
$|{PQ} ^{ \to} \times {PS}^{ \to}|$
Here, ${PQ} ^{ \to} = \lt 2,3 ,1\gt$
${PS} ^{ \to} = \lt 4,2,5 \gt$
${PQ} ^{ \to} \times {PS}^{ \to}=|\lt 2,3,1 \gt \times \lt 4,2,5 \gt| = \lt 13,-6,-8 \gt$
$|{PQ} ^{ \to} \times {PS}^{ \to}|=|\sqrt {13^2+(-6)^2+(-8)^2}| $
$= |\sqrt {169+36+64}|$
$=\sqrt {269}$ units
