\(AB=\sqrt{\left(1-3\right)^2+\left(5+4\right)^2}=\sqrt{85}\)
\(BC=\sqrt{\left(3-1\right)^2+\left(1-5\right)^2}=2\sqrt{5}\)
\(CA=\sqrt{\left(3-3\right)^2+\left(-4-1\right)^2}=5\)
\(p=\frac{\sqrt{85}+2\sqrt{5}+5}{2}\)
\(p-AB=\frac{2\sqrt{5}+5-\sqrt{85}}{2};p-BC=\frac{\sqrt{85}+5-2\sqrt{5}}{2};p-CA=\frac{\sqrt{85}+2\sqrt{5}-5}{2}\)
\(\Rightarrow S_{ABC}=\sqrt{p\left(p-AB\right)\left(p-BC\right)\left(p-CA\right)}=...\)