Hi everybody. As a beginner I tried different approaches to this topic but was unable to obtain desired result.
Problem: I got 4 intersecting bezier curves ( intersecting like in the symbol # ; with 4 intersection points: see attached svg file).
I need to obtain a 4 "sided" closed path (the area enclosed by "trimmed" beziers).
Inset, combine or union do not provide the desired result.
Any suggestions ?

There may be several ways to do this.
But out of curiosity, before I share my thoughts, wouldn't it be simpler to make a square, and then Object to Path?

If you just need to fill the area you could use the . If that is not precise enough. Duplicate you 4 paths and move them to a new layer just to be safe. Do a stoke to path under path menu. (Ignore this step since they are not strokes.) Then select all 4 paths do a union on the paths. Finally do a break apart also under paths. You'll have two paths now. You wont be able to see until you move one. One a black box one a black box with 4 lines coming out of the corners. The other one is the path you were looking for. If they were stokes how you'd do this would be totally different.

Edit: I just notices your paths were closed fill paths not stokes? I think that might have been part of your problem.

Thanks EarlyBlake :as suggested Union + break apart works perfectly.

Note: I needed it as I' working on an existing monochrome vector image that already contained these paths (the attached svg is just an example) ; obtaining closed paths this way is much easier than redrawing parts of the image !