Dropped third strike

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Had this situation come up in a 11-12 year old tournment game. FED Rules Runners second and third 1 out 2-2 count pitch comes in batter swings and misses and the catcher drops the ball, un aware of this the batter turns towards the dugout when finally one of his teamates screams run to first by this time however he has already reached the on deck circle. Now according to the rule book it says a batter is not out on a dropped third strike until he has reached the dugout or bench area. The kid beat the throw to first, so now the opposing coach comes out and begins to argue that the on deck circle is part of the bench area. I cant seem to find a rule defining bench area, does it mean the exact same thing as dugout or not.