How to fill region defined by several smooth plot tikz

Question

I am having problems filling the region below that is given by 4 paths with known intersection points.

After playing around with clipping and doing my due diligence searching the forums I am still at a loss.

Any help would be appreciated.

\documentclass{minimal}
\usepackage{tikz}

\begin{document}


$$
\begin{tikzpicture}

\draw (22.5:4) -- (22.5:9);
\draw (67.5:4) -- (67.5:9);

\draw plot [smooth] coordinates 
{(22.5:4) (30:3) (55:3) (67.5:4) };

\draw plot [smooth] coordinates 
{(22.5:9) (33:7.5) (50:10) (60:8) (67.5:9) };

\end{tikzpicture}
$$

\end{document}

Answer 1

You are almost there. If you do the reordering of the drawing inside one single path then it is clear :)

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}

\draw[fill=red] (22.5:9) -- plot [smooth] coordinates {(22.5:4) (30:3) (55:3) (67.5:4) } 
         plot [smooth] coordinates {(22.5:9) (33:7.5) (50:10) (60:8) (67.5:9) } -- (67.5:4);

\end{tikzpicture}
\end{document}

PS: Don't use minimal class. It is a minimal for LaTeX developers to test dependencies not meant for users. It might cause problems and you wouldn't suspect it. The real minimal class for the end users can be considered to be article or standalone.