Final answer:
The Shang Dynasty controlled a large area by utilizing a strong military, advanced agricultural methods, central government, and theocratic rule to maintain power and manage their territory effectively.
Step-by-step explanation:
The Shang Dynasty maintained control over a large area through a combination of military prowess, advanced agricultural techniques, a centralized government, and an aristocratic class that oversaw the kingdom’s activities, including religion and warfare. A strong military including bronze weaponry and chariots was crucial for both expansion and defense, while good farming methods ensured food surplus to sustain the population. Additionally, the Shang established centralized governance with a noble warrior class controlling the administration, and rituals centered around the worship of ancestors and the supreme deity Di which united the people under a theocratic system. The dynasty's power was further reinforced by its monopoly on the use of bronze and the creation of large-scale defensive structures such as city walls, which required organized labor and demonstrated the Shang's organizational capabilities.