4. Among the following four figures, which one has the largest area?
A. $\triangle A B C: \angle A=60^{\circ}, \angle B=45^{\circ}, A C=\sqrt{2}$
B. Trapezoid: The lengths of the two diagonals are $\sqrt{2}$ and $\sqrt{3}$, and the angle between them is $75^{\circ}$
C. Circle: Radius is 1
D. Square: The length of the diagonal is 2.5
For option $A: \frac{B C}{\sin A}=\frac{A C}{\sin B} \Rightarrow B C=\sqrt{3}, C=75^{\circ}$
$$
\Rightarrow S_{\triangle A B C}=\frac{1}{2} \cdot \sqrt{2} \cdot \sqrt{3} \cdot \frac{\sqrt{6}+\sqrt{2}}{4}=\frac{3+\sqrt{3}}{4} \text {; }
$$

For option $B$: As shown in the figure, construct $\square B E C D \Rightarrow S_{\triangle A C D}=S_{\triangle C B E}$
$$
\begin{array}{l}
\Rightarrow S_{\text {trapezoid } A B C D}=S_{\triangle A C E}=\frac{1}{2} \cdot \sqrt{2} \cdot \sqrt{3} \cdot \frac{\sqrt{6}+\sqrt{2}}{4} \\
=\frac{3+\sqrt{3}}{4}<\frac{5}{4}=1.25 ;
\end{array}
$$

For option $C: S_{\text {circle }}=\pi$; For option $D: S_{\text {square }}=\left(\frac{5}{2} \cdot \frac{\sqrt{2}}{2}\right)^{2}=\frac{25}{8}$. Comparing these, $S_{\text {circle }}=\pi$ is the largest, so the answer is $C$.