There are two ways to measure rib eye area (REA). Traditionally, REA is measured by making a cut at the 12th rib on a beef carcass and measuring the area in square inches using a grid like the one pictured at http://www.flickr.com/photos/baalands/2348385410/. Other species are not cut and measured on the hanging carcass as a standard practice.
The second method can be used on live animals and involves ultrasound. A trained technician will create an image of the rib eye at the 12th rib. Other information is necessary, including the age and weight of the animal when it is scanned. Using a standardized formula, the area of the rib eye can be calculated. This second method is most often used on animals that are going to be used in a breeding herd and allows a producer to make decisions about the best animals to keep.