Close and Open geometrical figure

Off the top of my head, a closed figure is a figure whose perimeter begins and ends at the same point (on 2D plane).

Ard hope this might help

http://www.google.ca/#hl=en&output=search&sclient=psy-ab&q=define+of+closed+figure+in+2d+plane&oq=definition+of+closed+figure+in+2D+plane&gs_l=hp.1.0.33i29i30.2057.2057.0.5367.1.1.0.0.0.0.156.156.0j1.1.0...0.0...1c.2.7.psy-ab.4r36iDjVDXU&pbx=1&bav=on.2,or.r_qf.&bvm=bv.44158598,d.cGE&fp=3bbcd90b84c3d114&biw=1197&bih=540

In what way is your exasperating links useful, Dale?

Look what your first result is :



Please, stop those unbelievable dumb url's.

Mathworld (Wolfram) includes this on the polygon page:
There is unfortunately substantial disagreement over the definition of a polygon. Other sources commonly define a polygon (in the sense illustrated above) as a "closed plane figure with straight edges" (Gellert et al. 1989, p. 162), "a closed plane figure bounded by straight line segments as its sides" (Bronshtein et al. 2003, p. 137), or "a closed plane figure bounded by three or more line segments that terminate in pairs at the same number of vertices, and do not intersect other than at their vertices" (Borowski and Borwein 2005, p. 573). These definitions all imply that a polygon is a set of line segments plus the region they enclose, though they never define precisely what is meant by "closed plane figure" and universally depict polygons as a closed broken black lines with no shading of the interiors.