The youngest child of KingFolcwine of Rohan. When Fengel was just fifteen years old, the Haradrim launched an attack on Gondor, and StewardTúrin II sent to Rohan for aid. Fengel's elder brothers Folcred and Fastred answered the call, but were both slain in battle, and thus young Fengel became his father's heir.
When he eventually succeeded to the throne to become Rohan's fifteenth King, Fengel proved a foolish and wasteful ruler, and was most noted by history for his greed. He quarreled with his advisors, and had little respect from either his Marshals or his children. Indeed, his son Thengel left his father's court as soon as he reached manhood, and served StewardTurgon in Gondor until his father's death.
During the later years of Fengel's rule, Sauron was driven out of Dol Guldur by the White Council, and returned to his old land of Mordor. Thus a grave new threat emerged to both Rohan and Gondor, but Fengel did not have to face that threat; he died just two years after Sauron's return.
Though fengel can mean either 'king' or 'prince', the latter is more likely in this case. When Fengel was born he had two valiant elder brothers, so his chances of becoming King would have seemed slight at the time he was named.
2
The dates of Fengel's elder sister are not recorded, and so it is not inconceivable that she was Folcwine's eldest child. We do, however, have dates of birth for the twins Folcred and Fastred (III 2858) and for Fengel himself (III 2870). Given the gap of twelve years, it seems reasonable to assume that the only daughter of Folcwine was born at some point between these two dates.