Test if a 3D Point is with an extruded "2.5D" Polygon

I need to check if a point given as x,y,z coordinates is within an extruded 2.5D Polygon. I thought it should be possible to achieve using a 2D point-in-polygon check (e.g. [1]) with additional distance checks.

I'd like to avoid creating meshes for the polygon for performance reasons. Is it possible?

[1] How can I determine whether a 2D Point is within a Polygon?