Is it possible to find the area of a triangle from the length of one side and the measure of the opposite angle?

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Sorry for maybe stupid question, because I'm pretty sure the context is incomplete, but anyway.

Given $$ \triangle ABC; AC = 4 cm; \angle ABC = 45°; S \triangle ABC-? $$

That's all. Is there a way to solve this?

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Hint:

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That's right, there in not enough data to find the area of $\triangle ABC$, however, we can state that it can't be greater than \begin{align} S_{ABC} &\le \tfrac14\,|AC|^2\,\cot\tfrac12\angle ABC . \end{align}