3. If the coordinates of the vertices of quadrilateral $A B C D$ are $A(1,2)$, $B(2,5)$, $C(7,3)$, and $D(5,1)$, find the area of quadrilateral $A B C D$.
3. As shown in Figure 5, construct the circumscribed rectangle of quadrilateral $ABCD$, with its vertices at $M(1,1)$, $N(1,5)$, $P(7,5)$, and $T(7,1)$. Quadrilateral $ABCD$ is obtained by removing $\triangle AMD$, $\triangle ANB$, $\triangle BPC$, and $\triangle CTD$ from rectangle $MNPT$. It is easy to see that
$$
\begin{array}{l}
S_{\text {quadrilateral } MNPT}=24, S_{\triangle AMD}=2, S_{\triangle ANB}=\frac{3}{2}, \\
S_{\triangle BPC}=5, S_{\triangle CTD}=2 .
\end{array}
$$

Therefore, $S_{\text {quadrilateral } ABCD}=24-\left(2+\frac{3}{2}+5+2\right)=\frac{27}{2}$.