I cant believe how many people are trying to offer up third party solutions to a question that was answered correctly in the first post...use the TV's resolution. If you are going to run it form a laptop, use whatever resolution the laptop and TV will agree on without aspect issues. You set your flash document resolution in the properties panel at the bottom of the application screen (default).
High-Definition Display Resolutions
Resolution (WxH) Pixels Aspect Ratio Video Format Description
1024×768 786,432 16:9 (non-square pixels) 720p/XGA Used on PDP HDTV displays with non square pixels
1280×720 921,600 16:9 720p/WXGA Used on Digital television, DLP, LCD and LCOS projection HDTV displays
1366×768 1,049,088 16:9 720p/WXGA - HDTV standard format Used on LCD/PDP HDTV displays (HD Ready, HD Ready 720p,1080i)
1024×1080 1,105,920 16:9 (non-square pixels) 1080p Used on PDP HDTV displays (Full HD, HD Ready 1080p)
1280×1080 1,382,400 16:9 (non-square pixels) 1080p Used on PDP HDTV displays (Full HD, HD Ready 1080p)
1920×1080 2,073,600 16:9 1080p - HDTV standard format Used on all types of HDTV technologies (Full HD, HD Ready 1080p)
4096x2160 8,847,360 16:9 2160p DCI Cinnema 4k standard format Quad HDTV, (there is no HD Ready 2160p Quad HDTV format)
You can google or Wiki the rest, i hope.
Anyway...once you make your FLA set to these dimensions, the exported video, etc will be the appropriate resolution. Using the NATIVE resolution of the TV will give you the best picture overall.
As to the "why flash" question...
how do you videotape a powerpoint?
How do you interact with a pre-recorded video?
Flash has more bells and whistles like being able to thread live video through itself while playing a pre-recorded one to give both a live and pre-recorded experience in one screen, complete with the potential for using changes in the atmospheric video (via Bitmap array mathematics) to create live responses in the Flash one, or even just have simple butten state interactions that show guided content based on realtime curiosity of visitors to your booth. Do that with your handicam!
Peace,
Julian Santa-Rita
//who has had to do this for tradeshows too
p.s.
if you e-mail me i'll send you my FLA's for example
juliansr@mwyusa.com