Answer
$6.576$
Work Step by Step
The cross product is defined as:
$u \times v=\begin{vmatrix}i&j&k\\m_1&m_2&m_3\\n_1&n_2&n_3\end{vmatrix}=\lt m_2n_3-m_3n_2, m_3n_1-m_1n_3, m_1n_2-m_2b_1 \gt$
The area of a triangle $A$ is defined as the length of the cross product $A=\dfrac{|u \times v|}{2}$ .
Now,
$u \times v=\begin{vmatrix}i&j&k\\-2&-1&2\\-2&3&-3\end{vmatrix}=(3-6)i-(6+4)j+(-6-2)k=-3i-10j-8k$
Then, we have
$A=\dfrac{|u \times v|}{2}=\dfrac{\sqrt{(-3)^2+(-10)^2+(-8)^2}}{2}$
or, $A=\dfrac{\sqrt{173}}{2} \approx 6.576$
