18. Determine the area of triangle $ABC$, if $A(1 ; 2)$, $B(-2 ; 5)$ and $C(4 ;-2)$.
Solution. Let's form a column:

![](https://cdn.mathpix.com/cropped/2024_05_21_b1a79769c6c63d19f37fg-17.jpg?height=211&width=234&top_left_y=380&top_left_x=911)

From here, \( F_{\mathbf{s}} = ((-2 + 20 - 4) - (8 + 4 + 5)) = -3 \).

By formula (4), \( S_{A B C} = \frac{1}{2} \cdot |-3| = 1.5 \).