Problem 11. Find the area of triangle $ABC$, if $A(3, -1)$, $B(1, -3)$, $C(-6, 6)$.
Solution. Let's complete triangle $A B C$ to form a rectangle $C M K P$ (Fig. 10). Obviously,

$$
\begin{gathered}
S_{A B C}=S_{C P K M}-S_{C M B}-S_{B A K}-S_{A C P}= \\
=9 \cdot 9-0.5 \cdot 9 \cdot 4-0.5 \cdot 2 \cdot 2-0.5 \cdot 9 \cdot 7=29.5
\end{gathered}
$$