Completely Filling Custom Geometries

I'm trying to figure out how to completely fill a custom geometry. It seems like it should be a common question, but I haven't really been able to find any solutions.

I have the following example geometry:

    <Path Fill="White" Stretch="Fill" Stroke="Black" StrokeThickness="2">
        <Path.Data>
            <PathGeometry
                Figures="M112,296C112,296 136,296 136,320 M112,344C112,344 136,344 136,320 M112,296L112,296 96,296 96,344 112,344"/>
        </Path.Data>
    </Path>

Which produces the following result:

This is the result I would like to see:

Any Ideas? I know I could make a single arc and that would resolve this particular case, but in my application the user can draw any type of geometry so the result could be composed of any number of "primitives" (PolyLineSegments, EllipseGeometries, ArcSegments, etc) and in the case that the resultant geometry contains some type of closed area, I'd like to accurately fill that area.

EDIT:

Here is an example of what a CombinedGeometry looks like if I ensure all three adjacent geometries overlap and create a unioned CombinedGeometry with the following code:

        <Path Grid.Row="2" Fill="White" Stretch="Fill" Stroke="Black" StrokeThickness="2">
        <Path.Data>
            <CombinedGeometry GeometryCombineMode="Union">
                <CombinedGeometry.Geometry1>
                    <CombinedGeometry GeometryCombineMode="Union">
                        <CombinedGeometry.Geometry1>
                            <PathGeometry
                                Figures="M111,293C111,296 136,293 136,325"/>
                        </CombinedGeometry.Geometry1>