Best method; slice and dice, pathfinder ....?

So I am doing a geological section in which there are several layers/strata/zones with odd shapes (similar to a jigsaw puzzle).

I began by drawing the overall perimeter of the area and then drawing open paths depicting the common boundaries of the strata. Now I need to subdivide the overall perimeter into pieces so that each area can be given a specific fill.

I imagine there are different methods/tools to use to accomplish this so I would like to use the one that would be the quickest and easiest to use.

I will try and attach an example file which I began but have not finished.

Any tips would be appreciated.

Sorry I have been away for a few days. Without knowing the zones I would not like to complete this drawing for you but I would like to! Right you have made a good start but all you have got is open lines with the main datum complete and this means using the Pen Tool to try a close the paths. I always don't care where I draw lines to connect and close the paths that can be sorted later so roughly trace over the outlines and if you want you can join the lines using the direct selection tool Shift click 2 open end points that you want to join then hold down Ctrl+J to join. You may only need to join 2 lines together to get your fill to work. Really when you import your data in (hand drawn sketch) think about your colour fills to shown the different stratas and use the Pen Tool to roughly copy these in don't worry about being accurate here as once you have it closed then you can select the Nodes with the Direct Selection Tool (A) to edit the shape to make it then accurate. Now if you have smaller areas which lie on top of a coloured strata put then areas on a different layer and lock the main statas so they are not selected.

Now the Pathfinder Tool is your best friend John and it is very powerful much more powerful than, as I know you use Xara, the Combine Shapes command but it does the same thing and more!
Slice & Dice is only for the web so don't use that tool!
You can use the rubber, scissors and the kniefe tool but have a look at the Help file for the use of the tools.

Learn to use the Pen Tool and if you want a curve line press on the "Shift" and drag.