Elementary Geometry for College Students (6th Edition)

The area of the parallelogram is $2\times \frac{1}{2}a\times b \times sin\gamma$
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.