I am having some trouble adding the following geometry to my model:
The problem in the picture is that the gray geometry isn't connected to the black part of the model. I'm doing some bevel work, and it needs to be connected. I tried using a knife project of the shape, and extruding it from the model. But I had trouble getting all of my faces to stay flat. It created weird artifacts. I also tried using boolean operations to connect the gray part to the model, but the boolean operation failed, and I couldn't figure out a way for that to work either. I am not sure how to solve this.
I feel like there is a better solution; everything I have tried so far has produced artifacts. Are there any modeling techniques for extruding this kind of geometry? Or is there some other way for me to attach the gray mesh to the rest of the model?