Although very late, but you could do something like this with some Python code:
import arcpy
import os
workspace = r"C:\Path\To\Your\Folder"
sum_areas = 0
cnt = 0
walk = arcpy.da.Walk(workspace, topdown=True, datatype="FeatureClass", type="Polygon")
for dirpath, dirnames, filenames in walk:
for filename in filenames:
cnt += 1
shp = os.path.join(dirpath, filename)
area = sum([r[0] for r in arcpy.da.SearchCursor(shp, ("SHAPE@AREA")) if not r[0] is None])
sum_areas += area
print "shp: {0} has area {1}".format(shp, area)
print "{0} polygon featureclasses found".format(cnt)
if cnt > 0:
print "total area: {0}".format(sum_areas)
print "mean area per featureclass: {0}".format(round(sum_areas / float(cnt),2))
