Answer
The area of the parallelogram is $2\times \frac{1}{2}a\times b \times sin\gamma$
Work Step by Step
In order to calculate the area of the parallelogram, we have to calculate the area of the two triangles $\triangle MNQ$ and $\triangle PQN$.
$MN=QP=b$, $MQ=NP=a$ and $\angle QMN =\angle NPQ = \gamma$ because $MNQP$ is a parallelogram.
So, the area of both triangles can be calculated by $\frac{1}{2}a\times b \times sin\gamma$.
The area of the parallelogram is $2\times \frac{1}{2}a\times b \times sin\gamma$ which is exactly the given formula.
