I did some testing. Took my hit area weapon into a spawn and was watching for the hit area damage vs the amount from the hit.
I can definitively say that the bigger the first hit is, the more the hit area damage is.
I am nearly certain that the damage is also modified by the hit area % of the weapon as well. Here's my logic. In level 1 of the 'Coon spawn, we get slimes and giant rats. The damage being done to the mobs is errily almost exactly (damage from my hit) * (weapons chance to hit area) * (1- resist of nearby stuff). For instance, against a lizardman with a hit cold area, I did 69 damage from the swing, and 30 from the hit area. Then I decided to look at a 100% hit area, so I found my serpent fang and the hit area from this was just about the same ration as from my other attempt.
It would seem, then, that hit area damage is always 50% of the weapon damage, then factor in the armor rating of the target. I did not bother to try anything with SDI on it...