\(AB=\sqrt{\left(1+1\right)^2+\left(2-2\right)^2}=2\)
\(AC=\sqrt{\left(2+1\right)^2+\left(-3-2\right)^2}=\sqrt{34}\)
\(BC=\sqrt{\left(2-1\right)^2+\left(-3-2\right)^2}=\sqrt{26}\)
\(cosBAC=\dfrac{AB^2+AC^2-BC^2}{2\cdot AB\cdot AC}=\dfrac{3}{\sqrt{34}}\)
=>\(sinBAC=\dfrac{5\sqrt{34}}{34}\)
\(S_{ABC}=\dfrac{1}{2}\cdot2\cdot\sqrt{34}\cdot\dfrac{5}{\sqrt{34}}=5\)