Planar Graphs · Challenge problem

Let $G$ be the graph on vertices $0,1,\ldots,8$ forming the $9$-cycle ($01,12,23,34,45,56,67,78,80$) together with the two chords $04$ and $27$. Using $G$'s girth in the general edge bound $E \le \frac{g}{g-2}(V-2)$, what is the largest possible integer value of $E$ for a connected simple PLANAR graph on $9$ vertices with the same girth as $G$?