If you draw your arc on the piece, get your Push/Pull tool, then tap the [CTRL] key you should be able to push the arc through leaving some stuff on the underside. Now select the part and all of the stuff that was added by the Push/Pull and intersect with selected. Now carefully erase your unneeded geometry being careful not to delete the arc intersecting the underside of the surface. That arc completes the bottom surface and you should be good to go.