Using the image in Doug B's answer, we can attempt to determine the size by using the door as the scale, given that they are both nearly the same distance from the camera (the door being a little closer).
Based on other clips, the doors appear to be roughly 6'8" in height. Jonathan Frakes is 6'4", and the top of the door appears to be a few inches higher than his head. If we account for shoe height, and that the average American door is 6'8", this seems like a reasonable assumption.
The screen is taller than the door in the background (and roughly the same distance back back at the center of each). Measuring the height of each at the center in pixels, the screen appears to be very close to 8 feet in height. Likewise, on it's side and scaled for the angle, it appears to be roughly 2.5 door-heights wide (around 16'6").
While not definitive, I would put it at 8 x 16.5 feet (which would be a 16:33 aspect ratio).
Praxis gives a definitive answer, which is within about .75 feet of this estimate (8'2.5" tall, 15'9" wide).