\begin{aligned} \vec{a} &= \overrightarrow{AB} = B - A \\[8pt] &= (4,1,-2)-(3,8,2) = (1,-7,-4) \\[8pt] \vec{b} &= \overrightarrow{AC} = C - A \\[8pt] &= (-1,3,5)-(3,8,2) = (-4,-5,3) \\[8pt] \vec{a} \times \vec{b} &= \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\[5pt] 1 & -7 & -4 \\ -4 & -5 & 3 \end{vmatrix} \begin{matrix} \hat{i} & \hat{j} \\[5pt] 1 & -7 \\ -4 & -5 \end{matrix} \\[8pt] &= \left( (-7)(3)-(-5)(-4) \right) \hat{i} + \left( (-4)(-4)-(3)(1) \right) \hat{j} + \left( (1)(-5)-(-4)(-7) \right) \hat{k} \\[8pt] &= (-21-20) \hat{i} + (16-3) \hat{j} + (-5-28) \hat{k} \\[8pt] &= -41 \hat{i} + 13 \hat{j} - 33 \hat{k} \\[8pt] |\vec{a} \times \vec{b}| &= \sqrt{(-41)^2+13^2+(-33)^2} = \sqrt{2.939} = 54,21 \\[8pt] \text{Luas ABC} &= \frac{1}{2} |\vec{a} \times \vec{b}|=\frac{1}{2} \cdot 54,21 = 27,1 \end{aligned}