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The item you want to have filled should be created with one call to
cairo_moveto, the rest should only be cairo_lineto.
The first cairo_moveto of your path definition also defines the endpoint,
i.e. the point wich is used to close the element in order to fill.

For the given points

A            D
   |       |
B --------- E
   |       |
C --------- F

I _think_ the correct sequence should be

moveto (A)
lineto (B)
lineto (C)
lineto (F)
lineto (E)
lineto (D)

// needed to only fill the BECF rectangle
lineto (E)
lineto (B)

closepath


Regards
Dirk