You are right you have to use thresholded output of maxent. Convert this from ascii to raster in arc (do not forget to check the integer raster option in arc) , then convert this raster to polygon (uncheck simplify polygons) and then calculate the area of all polygons with gridcode=1. This is the area of your thresholded species distribution model.
Regards
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I also want to add that if you interpret this thresholded raster as the area your species can occur in, presumay using the logistic threshold, there are various assumptions you are making. Please read through Merow et al. 2013 in Methods in Ecology & Evolution before affirming your interpretation.
Jamie Kass
PhD Student
City College of NY