The human prince on the painting doesn't look 11 years old. He looks older, perhaps about 16-18.

I think paintings in that time period, some at least, were often painted so the subject was often portrayed as slightly older, or younger, or skinnier, ect. I think that maybe it portrayed him as a little older than he was. If you take into account sequels, and I do, in The Enchanted Christmas he looks to be about 11 when the Enchantress comes to the door.

I believe he was 11, but he looks older, I've always thought so.

I agree with @auroraxaurelia
I really like the idea that Beast was cursed for a decade because it makes his salvation so much more important to him and his actions in the 3rd act (Letting Belle go) becomes more noble (But I agree that The Enchantress putting a spell on a kid is a bit extreme but it is a Fairy Tale so I don't think about it too much)

I think he was somewhere in the middle, about 13 or 14.