The simplest method would be to use Fill Holes to fill all the holes after you threshold. Another tool that might be useful is Convex, which fills in any concave surfaces on the edge of your object. This will only work with convex objects, though.
After using these routines, just use Quantify or Particle Analysis to get the area of the object. I would probably use Particle Analysis and search for the largest object to eliminate any small particles stuck to your background.
Bruce
Bruce Ammons
Ammons Engineering