You have to add an attribute field for the Area (in whatever units you want) to your layer first, and calculate the areas, before it will be available as a piece of data you can see when you're viewing the layer. A layer in a file geodatabase will already contain a field for the shape's area (Shape_Area) but if you want a different unit of measurement you need to add your own field.
- Right-click your layer and select Open Attribute Table.
- In the Table window, click the button in the upper-left corner (Table Options), select Add Field.
- Name the field whatever you like ("Acres"), set the Type to a number field with the level of precision you want. I'd just use Double. Click OK.
- Right-click the header of your new field, click Calculate Geometry, choose Area as the property, then Acres as the units. Click OK and your new field will be populated with the acreages of the polygons.
Important: this area is not automatically updated, if you edit the polygons, or add new ones, you'll need to recalculate. The Shape_Area field, on the other hand, is automatically updated if the layer is edited.
You can also install the Xtools Pro extension, it has many free features, one of them lets you easily add Perimeter, Length, and Area to your layer's attribute tables all at once, in whatever units you want.