Wanted to check if there is a way to achieve (b) by joining dots (a) in Inkscape.
I am not quite sure if this is always trivial, but you can try something like the following:
Select the shape and Path > Break apart (or Shift CtrlK).
Select the horizontal part and duplicate it Ctrld.
Select the vertical part and duplicate it Ctrld.
Combine the horizontal part: CtrlK and select: Extensions > Render > Frame and press Apply.
Repeat that for the vertical part.
Ungroup the results and align the rectangle shapes as shown below, then Path > Union.
To be able to fill the shape, select it then Path > Stroke to path and break apart Shift CtrlK
Ungroup the result, and remove the bottom shape. Select the remaining shape and choose: Path > Stroke to Path then break apart Shift CtrlK
The animation was divided to two parts to be able to upload it (2MB limit).