Parallelogram Area via Two Sides and Included Angle

A parallelogram is defined as a quadrilateral with two pairs of parallel and congruent sides.

What shapes is a parallelogram composed of?

A parallelogram can be split into two triangles that are congruent, by $SSS:$

Keeping this in mind, is there a formula we could come up with to express the area of a parallelogram in terms of only its sides and angles?

Yes! Let $\angle ABC = \theta$ in the diagram above. Then, $$\begin{align} [ABC] &= \left(\dfrac{AB\cdot BC}{2}\right)\sin \theta \\ &= [ADC] \\ [ABC] + [ADC] &= [ABCD] \\ &= (AB\cdot BC) \sin\theta \end{align}$$

So the area of a parallelogram is equal to the product of two of its adjacent sides and the sine of their included angle, or $AB\cdot AC \cdot \sin \theta$ for parallelogram $ABCD$ with $\angle ABC = \theta$.