Is my room 11 x 14, or 11 x 20?

I think it depends on what sound pressure level you want to listen at. The speakers are loading the entire space with sound waves unlike a room with a door that has a specific size and volume.(LxWxH). The distance you sit from the speakers also plays a part, you lose SPL with each meter you move away a vise-versa. Do you own a SPL meter? Most speakers have a good amount of leeway.

I believe the general rule when a room opens up to an adjoining room, is to reduce the volume of the adjoining room in half, and add that divided amount of space to main room's total volume.

Hodu - I think 11x14 is more relevant to your situation than the 11x20.

I'm in a ~13 x 15 foot alcove myself. Facing the speakers that are positioned 7-8 ft apart along the long wall (not ideal)the right (13') side wall of the rectangle is missing. The alcove opens into a much larger space on that side (probably 3x the area). There's a pocket door in the left wall that I keep open while listening + left speaker placement is a good few feet from the wall and corner (also have some DIY room treatment in the corner).

I consider my listening area, which seems like it might be even more "open" than yours, to be 13x15...and don't worry about the larger space outside it. Tom6897's point is a good one. I sit 7-8 feet or so from the speakers that are out (front plane) ~3' from the wall. I like to listen at volumes in the range of 78-85 db. No problem doing so in this setting. Hope this helps a little.

Neither. Your room is irregular shape. You can't use simple calculation to determine its effective size. You need to either run software simulation or do actual sonic measurement to find out its sonic characteristic.

Thanks for the responses -- I appreciate them.

Is there any wall on the side that opens up? I think you have two considerations. One is the volume of the room and the other is the sidewall reflections for speaker placement. If there is a stub wall or other projection, then I would position the speakers using that as my guide and forget the added area for positioning purposes.

Now, for loudness considerations and amp size, the recommendations above are good.