Final answer:
The best radiographic projection to demonstrate pneumoperitoneum in a patient able to stand is the AP erect abdomen, as it allows free air to rise and become visible under the diaphragm.
Step-by-step explanation:
To demonstrate the condition of pneumoperitoneum, the best projection for a patient who is able to stand would be the AP erect abdomen. This position allows any free air present in the abdominal cavity to rise and become visible under the diaphragm on the radiograph. When there is a concern for pneumoperitoneum, the radiologist would look for signs such as a crescent of air beneath the diaphragm or Rigler’s sign (gas outlining both sides of the bowel wall).