In architecture, a quadrangle (or colloquially, a quad) is a space or a courtyard, usually rectangular (square or oblong) in plan, the sides of which are entirely or mainly occupied by parts of a large building (or several smaller buildings).
The word "plan" is a noun, therefore I believe it to be a typo (no article). Another word that comes to mind is the word "plane" which is an adjective as well as a noun:
TFD def: noun
- Mathematics A surface containing all the straight lines that connect any two points on it.
- A flat or level surface.
TFD def: adjective
- Mathematics Of or being a figure lying in a plane: a plane curve.
- Flat; level. See Synonyms at level.
But these also don't fit for me somehow.