This requires a bit of Boolean magic, if you want to do it exactly.
So this is how I would do it:
Fix drawing:
- First, remove your lines. They do have a path effect applied, and they're not strictly horizontal, so not very good for dividing a continent :-)
- Duplicate (select, Ctrl+D) the continent border, and ungroup it, until it's just a path.
Create silhouette object:
- Select one duplicate, do Path -> Break apart
- Delete the inner section, or do Path -> Union with the two resulting shapes from Break apart.
Now you've got two objects above one another:
- the contour (which you had at the beginning, unchanged, at the bottom)
- a silhouette of the continent
Create stripes:
- Now duplicate the silhouette. You can also give it a different color.
- Now create a rectangle (with rectangle tool). Put it over the silhouette, so that it covers one stripe. It doesn't matter that it goes beyond the continent's borders.
- Select both the silhouette and the rectangle. Do Path -> Intersection. First stripe is done.
- Repeat the three steps in the last paragraph for the other two stripes. You can let them overlap a little to avoid ugly gaps.
In a last step, lower the stripes to the bottom, so they are below the original contour.