Two Triangles in a Decagon

Let $S$ be the area of the regular decagon.

Connect points $C$ and $F$. Since $AB$, $DE$, and is parallel to $CF$ from symmetry, we get that $S(ABC) = S(ABO) = S(DEO) = S(DEF) = S/10$.

Therefore, $80\%$ of the total area is shaded.