In Carolingian times, the yield of grain on average soil was 2:1. For each seed planted, you harvested two. Starting with the eleventh century, an upward trend brought agricultural productivity to an average of 4:1. This meant 8-12 bushels (200-300 kg) of grain per acre. Let's just conclude that in Carolingian times, in Western Europe, an acre of land gave 4-6 bushels (100-150 kg) of grain. Since it isn't clear whether the absolute yield increased or merely the seed-to-seed ratio. It might as well have been that the average Carolingian plot gave 8-12 bushels per acre, and half of it was kept as seed. Let's go with the second hypothesis, since an absolute yield of 4-6 bushels would have meant 2-3 used for consumption. Let's say an acre gave 8-12, and 4-6 were replanted the following year, whilst after the agricultural renaissance of the eleventh century, only 2-3 were replanted, leaving 6-9 for consumption.
An average human being required back then 14 to 24 bushels of grain per year to survive. Let's say children were situated at the lower margin, whilst full-fledged, hard-working adults at the upper one. Therefore, 4-6 acres were necessary to sustain an individual. Your household comprised of 2 adults and 2-3 children. You would have needed then 72-86 bushels per household - 12-22 acres. But then, again, I suppose that as absolute yield 8-12 is pretty high for the Dark Ages. I'd go with 6-8 bushels per acre gross yield, 3-4 net. This leaves a necessary of 6-8 acres per individual, circa 30 for a household. In the High Middle Ages, it is well known that 10-15 acres of land were necessary in order to sustain an average household.
Later edit: Oops! Sorry, I forgot to take into account crop rotation. Around half of the land was left fallow. The consequence of this is that even if in absolute terms 6-8 acres produced enough grain in order to feed an individual, his long-term needs of land were doubled - 12-16 acres (~5-6 hectares). Thus, an average household could have required even 50 or 60 acres (~20-25 hectares) of cropland.
"Life in a Medieval Village" by F. & G. Gies - a very accessible book, price- and content- wise, yet not lacking depth.
"Rural Economy and Country Life in the Medieval West" by G. Duby is a very thorough, sometimes husky piece of academic toil. (Pretty much all of the Annales School is obsessed with demographic and ecological macro-historical trends.)
"Early Medieval Settlements: The Archaeology of Rural Communities in North-West Europe, 400-900" by Helena Hamerow
"Peasants in the Middle Ages" by Werner Rosener
"The Agrarian History of Western Europe" by Slicher van Bath
"Peasant Life in the Medieval West" by Robert Fossier
"Medieval Farming and Technology: The Impact of Agricultural Change in Northwest Europe" by Grenville Astill and John Langdon