How wide you make the sides depends on the thickness of the sides.
Let's say the thickness is T.
Also, when you use "diameter" do you mean from flat-to-flat, or corner-to-corner ?
Let's assume you mean flat-to-flat.
Then, from the center axis to the outside flat surface will be 2.75" + T.
The outside corner-to-corner distance across the flat surface is:
2 x (2.75 + T)/(tan60)
= 2 x (2.75 + T)/1.732
= 1.155 x (2.75 + T) inches
Of course, you have to cut the sides with your table saw blade tilted 30 degrees, as you said.
The total circumference will be 6 times that value, or ... 6.93 x (2.75 + T) inches
I hope that I have done the trigonometery correctly !
As an example, suppose your thickness is 3/8" = 0.375". Your cut board width will be 3.609", and circumference is 21.654".
Does that seem right ? (Comparing circular cylinder with same wall thickness would have circumference of 19.635".)