you don't have to "redraw" over the lines with a POLYLINE.... just use the PEDIT command. this will allow you to convert and join your drawing into a polyline.
or you could use the REGION command, as long as all the lines/arcs are touching at an endpoint, it'll create a region for you to EXTRUDE.
so, my suggestion would be this: type REG in the command line, select your lines & arcs - now you have a region. next, type EXT in the command line, pick your new region, and set the hieght, and do a 3DORBIT to get a look at your newly extruded 3D object.