AutoCAD 2006 and access to the hatch area using API
The area is available but the property is available using the IAcadHatch2 interface. Here is a small sample in VBA showing it.
Sub Example_HatchAreas()
Dim oSset As AcadSelectionSet
Dim oHatch As IAcadHatch2
Set oSset = ThisDrawing.SelectionSets.Add("TEST_SSET1")
oSset.SelectOnScreen
For Each oHatch In oSset
Debug.Print oHatch.Area
Next
End Sub



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