Remove shape from body defined by points

[louisKC5QA]

I have a body that needs to have material removed from it to create a series of intersecting planes.  I have defined the geometry through sketches:

but extruding from the surfaces leaves artifacts because the extrusion is perpendicular to the final surface, not the body:

Is there a way to remove the material defined by the sketches completely?  Multiple extrusions to establish faces, then trying to remove the artifacts is not getting me where I need to be.

[davebYYPCU]

Extrude top profile, down to Object (sketch plane or surface body?)

or delete the sliver faces.

Might help....

[louisKC5QA]

Extruding from the top doesn't work.

Sliver faces will not delete.  Returns error "will not compute".  Moreover, I need the final faces to be perpendicular and parallel to the body, so extruding from the angled faces doesn't achieve this.

[davebYYPCU]

File > Export, and add to another message.

[wmhazzard]

Sweep the profile along an angled path.