Steve is correct as to the seams but a room of this size probably ought to be stretched in using tack strips all the way around. Otherwise it may not hold up in the long run.
You don't indicate if the floor is concrete or wood, but typically the pad would be stapled or glued down with carpet glue squirted out in a big S shape pattern under each roll of pad. Then stretch the carpet on top with tack strips.
If you absolutely want to use double sided tape to hold the pad and carpet down, then you must stick the pad down first and then stick the carpet down on top. I don't think you will get very long life with your double sided tape. It wouldn't make sense to stick one down and not the other cause the pad will bunch up underneath or the carpet will bulge above.
Go to your favorite home cheapo, and they probably have a list of carpet layers to recommend. They get around $3 to $4 a sq.yd. so you are looking at $30 to $50 bucks or so. You can probably find one who can come by some evening as it should only take an hour or so for a room of that size. Good carpet layers move very fast.
If nothing else, put your tack strips down about a finger depth away from the walls and use a knee kicker to stretch it in. Good luck.