We are told that our stomach actually takes a small percentage of our abdomen. Why is it that when we eat, our whole abdomen swells, instead of just the stomach area.

The stomach is a muscular organ and distends with food. The stomach is contained within the abdominal cavity- potentially spanning the left upper abdomen, the mid abdomen and the umbilical area(emphasis on "potentially"). This distending pressure is distributed equitably to the abdominal cavity thus making your abdomen distended when your stomach is filled with food. With time, food is emptied off the stomach into the intestines, and life goes back to normal.