Answer
$12.727$
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,
$u \times v=\begin{vmatrix}i&j&k\\4&1&1\\-1&2&2\end{vmatrix}=(2-2)i-(8+1)j+(8+1)k=-9j+9k$
Then, we have
$A=\dfrac{|u \times v|}{2}=\dfrac{\sqrt{(-9)^2+(9)^2}}{2}$
or, $A=\dfrac{9\sqrt{2}}{2} \approx 12.727$
