On a plate in the shape of an equilateral triangle $\text{ABC}$ with area $16\sqrt 3\;\text{sq cm}$, a rod $\text{GD}$, of height $8\:\text{cm}$, is fixed vertically at the centre of the triangle. $\text{G}$ is a point on the plate. If the areas of the triangles $\text{AGD} \:\text{and}\:\text{BGD}$ are both equal to $4\sqrt19;\text{sq cm}$, find the area of the triangle $\text{CGD}\:\text{(in sq cm)}$.
- $3 \sqrt {19}$
- $4 \sqrt {19}$
- $12 \sqrt {3}$
- None of these