Annulus
An annulus is a flat shape like a ring.

Area
Because it is a circle with a circular hole, you can calculate the area by subtracting the area of the "hole" from the big circle's area:
Area = πR^{2} − πr^{2}
= π( R^{2} − r^{2 })
Example: a steel pipe has an outside diameter (OD) of 100mm and an inside diameter (ID) of 80mm, what is the area of the cross section?
Convert diameter to radius for both outside and inside circles:
 R = 100 mm / 2 = 50 mm
 r = 80 mm / 2 = 40 mm
Now calculate area:
Area = π( R^{2}  r^{2 })
Area = 3.14159... × ( 50^{2} − 40^{2 })
Area = 3.14159... × (2500 − 1600)
Area = 3.14159... × 900
Area = 2827 mm^{2} (to nearest mm^{2})