I got 21589.18 sq.ft. Here's my calculations:
I used this diagram. First, it's obvious that C (look in diagram for area with letter c in it), is 5000pi, and that d is 100pi. Figure B is somewhat simple, because instead of trying to figure about A and B together, I split them apart. So since the central angle of sector B is 45 degrees, it's 1/8 of a full circle, making it's area 1250pi. the last part is stupid because of the square root of 2 making things complicated. Using geometric theorems (vert. angles, alt. interior, etc) it can be proved that the central angle of sector A is also 45 degrees, making it's area (1406.25pi-625pi * root2) When you add them all together you get 21590.178, rounded up is 21590.18.
Of course, logically the the cow can also graze in the small triangle next to the barn, adding 312.5 square units. But whatever, that's a technicality.
Hope I got it right. ;O