Autodesk Design Review has the ability to import a DWG or DXF file. It is automatically converted into a DWF and you can use all Design Review's tools.
If DWG TrueView is not good enough as it will only report the distance to the command line and the area command is pretty basic consider using Design Review instead.
Here is what the distance look like in DWG TrueView 2009. It is nice that it's now possible to measure but it's still not that user friendly.
And here is the area reported. Notice that for each point you snap there is no indication on where you snapped previously.
After importing a DWG into Autodesk Design Review 2009 it's a snap to measure, especially areas. Wish this was included in AutoCAD as well.