Straight Lines
Area of Quadrilateral via Diagonals
nta_pyq_2023_apr
Grade 11
Question:
The area of quadrilateral $ABCD$ with $A(2,1,1)$, $B(1,2,5)$, $C(-2,-3,5)$, $D(1,-6,-7)$ is equal to
48
$8\sqrt{38}$
54
$9\sqrt{38}$
Step-by-Step Solution
Key Concept: Area $=\frac{1}{2}|\vec{AC}\times\vec{BD}|$. $\vec{AC}=(-4,-4,4)$, $\vec{BD}=(0,-8,-12)$.
Area $=8\sqrt{38}$.
Correct Answer: 2