Question: How do I update the area field for a shapefile (i.e. after projecting the dataset or if there is no Shape_Area field to start with)?

Note: You can find the solution/method by searching in the ArcGIS Desktop Help. Go to the Index, search for the term "area", select the item "calculating for polygons, then select "Updating area for a shapefile".

Here is a slightly edited version of what is contained on that page:

1. Optionally, start an edit session in ArcMap. Calculating a field is faster outside of an edit session, but you won't be able to undo the calculation.
2. Open the attribute table of the layer you want to edit.
3. Right-click the field heading for area (if there is no field for area values, you can add a new field for area by clicking the Options button and selecting the "Add field..." - make sure you specify the field type as 'float' or 'double').
4. Click Calculate Values.
5. Check the Advanced box.
6. Type the following VBA statement in the first text box:

   Dim dblArea as double
   Dim pArea as IArea
   Set pArea = [shape]
   dblArea = pArea.area

7. Type the variable dblArea in the text box directly under the area field name.
   Click OK.

The field in your attribute table should now be filled in with the correct area values.