smc

Let $h$ be the height of the pyramid and $a$ be the distance from $h$ to $CD$. The side length of the base is $14$. The heights of $△ABE$ and $△CDE$ are $2\cdot 105÷14=15$ and $2\cdot 91÷14=13$, respectively. Consider a side view of the pyramid from $△BCE$. We have a systems of equations through the Pythagorean Theorem: $$\begin{gathered} 13^2-(14-a{)}^2=h^2 \\ 15^2-a^2=h^2 \end{gathered}$$ Setting them equal to each other and simplifying gives $-27+28a=225⟹a=9$. Therefore, $h=\sqrt{15^2-9^2}=12$, and the volume of the pyramid is $\frac{bh}{3}=\frac{12\cdot 196}{3}=\boxed{784}$.