I don't know of a built-in way to do it but it can be done using a script. If you create an Area Measurement comment you can then run a script on it that will calculate its total circumference length by calculating the length of each one of its sides, which are defined through an array of points (as the vertices property), and add them all up. It can then apply that value to the field's label, so you would have both the area and the circumference.
This can be done automatically for all comments of this type, once you create them, with a single click.
If you're interested in hiring a professional developer to create such a script for you, feel free to contact me privately by clicking on my username and then on Send a Message.