GRE: Can area of this parallelogram be known given one interior angle and the lengths of two adjacent sides?

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A GRE question asks whether the area of parallelogram can be found only using the information provided above.

Area of parallelogram = base x height

If we cut off one end to form a triangle and place it on the end, we would get a rectangle that looks like:

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But we still do not know the width of rectangle in order to calculate area. Can we assume that not enough information is provided?

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Yes, you can assume that. Just try two different $x$ values to demonstrate it.

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Area $A=54sin(x)$. Without knowing x we cannot find the area.