catcher's box

[uncas]

This may sound like a stupid question, but . . .
Isn't the catcher's box the rectangluar shaped box running from the plate area to about 3' behind? Isn't it formed by running lines 9' from the each middle corner of the plate to the plate's point on both the left and right sides? The Little League rulebook actually references the whole area as the catcher's box while I believe it is only the rectangle between and flowing behind the batters' boxes. I think the 9' lines are used to determine the outside bottom corners of the boxes,and that the whole area is not the catcher's box. Otherwise, the catcher would be able to position himself anywhere within an approximate 60 square foot area. A coach from another area insists the whole area is the box because that is what he learned in Williamsport in umpire training. I think he just wasted his money. Please advise.