Example 1 Given three points $A(2,1), B(3,2), C(1,4)$, find
$$S_{\triangle A B C}$$
$\begin{array}{l} \text { Solution: By Theorem } 1 \\ S_{\triangle A B C}=\frac{1}{2}\left|\begin{array}{llll}2 & 3 & 1 & 2 \\ 1 & 2 & 4 & 1\end{array}\right|=\frac{1}{2}(2 \times 2+3 \times \\ 4+1 \times 1-3 \times 1-1 \times 2-2 \times 4)=2 .\end{array}$