If you look north of the dancing faun you'll see a roped off mosaic floor backed by an eroded wall. Beyond the eroded wall you can see trees--that is the peristyle in the center of the house.
A peristyle is, basically, an open space surrounded by columns. The House of the Faun has two of these. The smallest, which is the one you can see over the wall, was about 20 meters east/west by 7 meters north/south. The reconstruction of this peristyle includes a formal garden; it may or may not have been a formal garden when it was in use.
Sources
For more on the archaeology of Pompeii, see Pompeii: Buried in Ashes.
Beard, Mary. 2008. The Fires of Vesuvius: Pompeii Lost and Found. Harvard University Press, Cambridge.
Christensen, Alexis. 2006. From palaces to Pompeii: The architectural and social context of Hellenistic floor mosaics in the House of the Faun. PhD dissertation, Department of Classics, Florida State University.
Mau, August. 1902. Pompeii, Its Life and Art. Translated by Francis Wiley Kelsey. The MacMillan Company.
