Is it greyed out because it's the auto-calculated Shape_Length field? You can't calculate that.
There are many ways to get the area, and it sounds like you've tried a few, but here are a couple more.
1.) Dissolve your polygons based on whether it's visible or not. If it's in a geodatabase, Shape_Length will show you the total.
2.) If your polygons are in a geodatabase, you can use Summary Statistics to group based on visible or not (case), and sum the Shape_Length.