Outside ring measurement is about 120 feet. Inside is about 80. The width is about 22. And just a ring arc. Not sure exactly what the complete circumference would be for either.

I can estimate it’s about 2200 taking the average of the inside and outside of the ring arc and multiplying by the width, but is there a more precise formula? Doesn’t have to be too exact.

The outside circle encloses an area PIR^2 where R is radius of outside.
Inside, similarly, is PIr^2
So area of donut is PI*(R^2-r^2)
Assuming edges of the segment are radii for the concentric arcs - that is, form 90º corners at each point, then multiply by the degrees of the segment over 360. i.e. a 90º segment is 1/4 of the donut area, a 120º is 1/3, 45 degrees is 1/8 and so on…

Depends how precise you want to be. At extremes, no. (consider a 1-foot radius and a 100 foot radius - the pie shape is effectively the area of a pie slice - PIR^2(arc degrees)/360; at the other extreme - say, 1000 feet and 999 feet radii - it’s about the same as the average length of the arc segment times 1 foot.

…Which is equal to R * piR(angle/360º), which is equal to the thickness (here equal to the radius) times the arc-length (piR(angle/360º). In other words, yes, you can, in all cases, just straighten out the lines, average them, and figure it as a rectangle, just like I and MikeS said.