Final answer:
King Arthur was supposed to have ruled during the 5th to 6th century AD, known as the Early Middle Ages.
Step-by-step explanation:
The century during which Arthur was supposed to have ruled is widely believed to be the 5th to 6th century AD. This period is known as the Early Middle Ages, a time of political and military upheaval in Europe. The legend of King Arthur and his Knights of the Round Table emerged during this era, although the historical accuracy of the story is still debated by scholars.