The area that was most affected by the spread of both Islam and Buddhism from 200 BC to AD 1450 is primarily Southeast Asia.
Buddhism spread throughout this region from India, gaining significant traction in areas like modern-day Thailand, Myanmar, Laos, Cambodia, and Vietnam by the early centuries AD.
Islam began to make its way into the region from the 7th century onward, particularly through trade routes across the Indian Ocean and through interactions with Arab traders. This led to the establishment of Islamic sultanates in places like Indonesia, Malaysia, and the Philippines.
Thus, Southeast Asia is the region most prominently influenced by both religious traditions during this time frame.