Field is huge, practically you can measure it with Total station by picking the co ordinates of boundry. - this is quickest way.
Other ways
Lengthy procedures
Measure angles of boundry line
Measure lengths with tape, rolling wheel, by foot steps etc.
While doing this inclination of ground should be accounted.
Then do calculation and calculate area of field.
No one have time today to measure acres of land manually, everyone want quick results.
Total Station will give you highly accurate results.
Other process like plane table survey, chain survey etc will give you still near to accuracy result but will take much more time.