Final answer:
Sir Gawain and the Green Knight was probably written between 1375 and 1400 A.D., late in the Middle English period, which is consistent with the era's focus on Arthurian legends.
Step-by-step explanation:
Sir Gawain and the Green Knight was probably written between 1375 and 1400 A.D. The poem is an important example of Middle English literature, which spans from approximately 1150 to 1500 A.D. This places the composition of Sir Gawain and the Green Knight toward the end of the Middle English period. The excerpt provided from Geoffrey Chaucer's The Canterbury Tales serves as a reference to the language and style of writing of that period, which Gawain also exemplifies.
The tale of Gawain is part of the rich Arthurian tradition, mentioning other notable characters such as Galahad and Lancelot, indicative of the era's literary focus. Although the exact author of Sir Gawain and the Green Knight is unknown, it is evident that the narrative was probably crafted during a time when stories of the Round Table were popular among the English-speaking audiences.