How's this room look acoustically?

Non parallell sides are good, but most of a rooms sound comes from the materials in the walls, so in effect, it's impossible to say how the room will sound just by the dimensions.
I'd put my gear bench up against the 4' wall and treat the wall behind me - the 9' wall with deadening material like mattresses etc.
It is a low ceiling over the 4' wall area but if its your gear it doesn't matter cos you can't walk there.
Hooray! Thank you John...the original idea comes from your studio site, actually...
What I was worried about is my barn has angled side walls like that, and it sounds terrible. So, cool, I think I'll go ahead with it...
Take the room out of the equation...

Hey, if you've got the money, buy some studio foam from Auralex. And some diffusors from them too. You can pretty much take any room out of the equation to translate sound and not color it. Idealy we'd record in a space with no walls and no floor and no ceiling, so if you put the right absorbers and diffusors, the room will not color the sound.