I have the following situation in Sketchup:
This is the situation I want to achieve (I didn't actually do this, I edited the lines out)
Is it possible to achieve this? I have tried joining, as cited by a source here but didn't find the Join tool mentioned. Whenever I simply remove the lines, the entire face of the horizontal bar gets removed with it. I don't want to stretch both the shapes out and ignore the problem because I ran into texturing issues doing this and I want to limit the number of faces rendered. I see no reason for those lines to be there.
After this, I want to stretch the now joined plane to create a thicker horizontal bar like in the image below. (I was trying to make a low-poly streetlight) I made this image by stretching both out and removing the lines afterwards, but when I looked inside of the model by hiding the front panel, there was a mess of lines where the smaller shape used to be that just couldn't be right.
You can shift+erase the offending lines to hide them.
What you really want, though, is to place the lamp post into its own group before creating the larger pentagon for the lamp. This will isolate lamp post from lamp and you can extrude the larger pentagon to from the lamp without dragging along the inner set of lines.