I know this doesn't solve the issue with shape area and perimeter, and this will probably be considered "the hard way", but I have a potential work around.
I've been working on a landscape plan from a scanned property survey. The survey has a "scale" graphic, and I included that graphic when I scanned the image. I drew a line across the scale and determined my ratio of line length to scale length. In my case it was 1" = 21.8'. So I could draw a line between 2 points, check the size of the line in the shape size and position window, multiply it by 21.8, and determine my real distance. Like I said, probably the "hard" way to do this, but it worked.