4. As shown in Figure 1, in quadrilateral $A B C D$, $\angle A C D=$ $20^{\circ}, \angle B D C=25^{\circ}, A C$ $=10, B D=8$. Then, the area of quadrilateral $A B C D$ is
(A) $40 \sqrt{2}$
(B) $20 \sqrt{2}$
(C) $18 \sqrt{2}$
(D) Uncertain
4. (B).
$$
\begin{aligned}
S= & \frac{1}{2} O C \cdot O D \cdot \sin \angle C O D+\frac{1}{2} O D \cdot O A \\
& \cdot \sin \angle D O A+\frac{1}{2} O A \cdot O B \cdot \sin \angle C O D \\
& +\frac{1}{2} O B \cdot O C \cdot \sin \angle D O A \\
= & \frac{1}{2} \sin 45^{\circ} \cdot(O C+O A)(O B+O D) \\
= & \frac{1}{4} \sqrt{2} A C \cdot B D=20 \sqrt{2} .
\end{aligned}
$$