The Collaborative International Dictionary of English v.0.48:

Perimeter \Per*im"e*ter\, n. [Gr. ?; peri` around + ? measure:
   cf. F. p['e]rim[`e]tre.]
   1. (Geom.) The outer boundary of a body or figure, or the sum
      of all the sides.
      [1913 Webster]

   2. An instrument for determining the extent and shape of the
      field of vision.
      [1913 Webster] Perimetric

WordNet (r) 3.0 (2006):

perimeter
    n 1: the boundary line or the area immediately inside the
         boundary [syn: margin, border, perimeter]
    2: a line enclosing a plane areas
    3: the size of something as given by the distance around it
       [syn: circumference, perimeter]

Moby Thesaurus II by Grady Ward, 1.0:

61 Moby Thesaurus words for "perimeter":
   alentours, ambience, ambit, border, borderlands, borderline,
   boundaries, boundary, bounds, bourn, bourns, brim, brink, circle,
   circuit, circumambiencies, circumference, circumjacencies,
   circumscription, circumstances, compass, confines, context,
   coordinates, edge, edges, entourage, environing circumstances,
   environment, environs, fringe, fringes, gestalt, habitat, hem,
   limitations, limits, marches, margin, metes, metes and bounds,
   milieu, neighborhood, outlines, outposts, outskirts, pale,
   parameters, periphery, precincts, purlieus, situation, skirt,
   skirts, suburbs, surroundings, total environment, verge, verges,
   vicinage, vicinity