I would say it's more likely to be your placement point that is out, rather than the center point of the polygon geometry.
Design Manager Streetscape Ltd
Solid Edge ST10 [MP7] Classic [x2 seats]
Windows 10 - Quadro P2000
Look at your command bar -- there are two options -- measure to corner or measure to flat. You are set to measure to flat. Change it to measure to corner and I think you will get the result you expect.
Whenever you enter a dimension for the polygon, you are not entering the dimension for the chord. Rather, the distance from the polygons center to the midpoint of the polygons chord (or the vertex depending on which option you have checked in the command bar) So, in your case if you get your Smart Dimension tool and first click on the center point of the polygon, then click on the midpoint of the chord, you will get the distance you originally entered.