Actually, that's not entirely true. There were two segments to the horizontal intermix chamber. One was built on set and was the forced perspective piece to which you are referring. The other segment, however, was a part of the background painting. I don't have it handy, but in the book
Mr. Scott's Guide to the Enterprise there is a photo of the intermix chamber. In that close-up still photo, you can clearly see where the physical set ends and the painting begins. In particular, the segments of the intermix chamber have subtle differences in the painted portion and the floor beneath it is plain in the painting portion whereas there is equipment in the floor of the actual set piece.
EDIT: I found the photo and (crudely) marked where you can see the edge of the painting against the set floor.
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