You can still edit the uv's if you want. Put your cursor somewhere within the uv editor and hold down your right mouse button. Select UV.
Now if you click where the lines are connected you can select individual uv's. You can also scale, translate, and rotate them like vertex points with the keys: w, e, r
Go ahead and scale the circles down so they're a little smaller. So that they fit in the bottom corner fo the second quadrant.
Notice how the top and bottom of our seat are literally projected ontop of one another. This is totally fine, acceptable, and encouraged. Overlapping uv's can save resolution space, and eventually make up for a higher detailed model
Now that we have the projection for the top and bottom of the sead finished, we're going to project the side of the seat.
Switch to component mode, and your selection mode to Face. Select the side of the seat.
Another easy way to select the side of the seat is to select the entire seat, then deselect the faces of the top and bottom from the uv texture editor. This will leave you with just the side selected
Notice how with the top and bottom of the seat we used the planar projection. This type of projection will not work for the side because it curves around. So for this case we will use a cylindrical projection.
From the menu under Edit Polygons, Texture, select Cylindrical Mapping
If you look in the uv texture editor, you will see that the uv's for the side are now projected and layed out
Just like the top and bottom of the seat, move the side of the seat to the third quadrant. And scale it so it fits well into the quadrant