Trigonometry · Challenge problem

Vectors $\mathbf u$ and $\mathbf v$ have $|\mathbf u| = 4$, $|\mathbf v| = 5$, and $\mathbf u\cdot\mathbf v = 12$. Find the area of the parallelogram whose sides are the vectors $\mathbf u + \mathbf v$ and $\mathbf u - \mathbf v$.