I got it to work, but it wasn't easy. I ended up with a bunch of holes on the sides and bottom. I was able to patch them up using triangles then smoothing coplanars. There were a couple of line discontinuities, which obviously turned into a surface once I filled the gaps. But around the edges of the holes on the side there were no apparent discontinuities, and I zoomed in pretty close to find them. What else could have caused those?

I've attached the file for reference. You can try intersecting those two shapes to see what happens.

Car Design 1.skp

@Dave R, thank you very much for your prompt reply. I tried erasing some faces and edges, it destroys the object. Looks like SketchUp Pro would be the way to go for this. I'll keep trying, but I don't think it's possible to do it in the free version.

I've done a fair bit of work in SketchUp, but I'm new to intersecting. I'm trying to "trim" a group using another group, keeping only what's common between the two. I know how to intersect the two and end up with line segments following the contour of the target group, but the problem I'm having is that both groups have smooth surfaces.

Case in point: I'm trying to design the body of a toy car. From the side, it looks a little like a rocket. From the top, it is shaped like a boat, with a flute-like hole through it. I was able to realize the side view and the flute hole, but not the boat shape. See the attached image for reference. Is it possible to create such a shape in the free version of SketchUp? I've watched some tutorials on YouTube, but none seemed to mimc the behavior I'm trying to achieve here.