In the figure, the triangles $ABC$ and $CDE$ are equilateral, with side lengths $1$ and $4$, respectively. Moreover, $B$, $C$ and $D$ are collinear and $F$ and $G$ are midpoints of $BC$ and $CD$, respectively. Let $P$ be the intersection point of $AF$ and $BE$. Determine the area of the shaded triangle $BPG$.