Proper way to convert lines to fillable shape?

[Contours]

I've tried various combinations of 'Join', 'Combine', 'Add' and 'Intersect' ... but I never end up with a shape that lets me left-click fill. Instead, the lines change color. I'll also mention that joining the endpoints of the lines isn't an option. The "cusps" have to be in the finished result.

I know this has to be simple. I just can't determine how to do it. (For my example result, I built a special shape behind the figure.)

Thanks in advance for help.