Offset curve on surface into "thickened curve"

I have the following curve (highlighted in green) on a surface:

I want to offset this curve on the surface on both sides to get a surface representing a “thickened curve”.

I can get the offset curves easily enough (the two red curves on each side of the green curve) but I’m lost as to how I can extract the region of the surface between them. (10.2 KB)

Like this? (15.3 KB)


Thanks @HS_Kim ! Very nice and simple solution. Didn’t think of using Pipe.

Just for added robustness, is there an alternate way of getting the section from the output of Split Brep that doesn’t rely on comparing areas? To account for the case where the section ends up being larger than the remaining surface.

Here’s another way… (21.4 KB)

That’s brilliant! Thank you very much!