This is  similar to the question I asked about fill at the beginning of this week - however the structure of the design is different.

Attached is the .svg file that was given after reading in a dxf file and then immediately filing it as an ,svg file.

This dxf file simply consists of a number of lines and arcs which form the sides of a number of closed shapes.  Most lines and arcs are part of the boundary of two closed shapes.  The .jpg file shows what is given when just one of the lines is selected,

As before, I want to be able to colour in the closed shapes in different colours.  I tried, selecting the fill shape and choosing a colour.  However, I got the Area is not bounded cannot fill  message.

I also tried some of the 'actions' which solved the similar problem when each of the closed shapes had a set of lines and arcs for their boundaries.  However, in spite of several attempts I could not get any sensible results.

I really would appreciate knowing:

1, if it is possible;
2. if so, the steps I would have to take - I do know it is more work but it would help if the steps could be totally defined as I find it difficult, at the moment, to understand general statements about what has to be done.

Thank you.

I'd approach like this:

• Select the lines needed to complete a single area and copy.
• Hide original layer.
• Paste-in-Place on a new layer. 
• Delete unneeded paths.

• Activate snapping to intersections.
• Select an overhanging curved path that is intersected by another path's endnode. (e.g. Select the top of the tee, not the upright.)
• Use the node tool to place a new node at the intersection.
• Delete the overhanging segment.

• Activate snapping to nodes
• Drag overhanging nodes ( having straight lines) to snap to corners.
• Use the select tool to select all paths
• Activate node tool.
• Select all nodes.
• Use "join selected nodes" button to merge nodes and paths.
• Select fill color.

Repeat for each area to complete a quarter of the design.

When one quarter is finished, it can be duplicated and rotated three times to complete the design.

Thank you - that really was very helpful.  It also showed me there was some symmetry to the design which I had not realised before!