Connor is building square decks. In the center of each deck, Connor places a square tile. The perimeter of the first 4 decks are shown in the table below. If Connor's rule to find the area of the square tile is to divide the area of the deck by 2, what would be the area of the tile for the seventh deck?
Let's first find the areas of the first 4 decks.
The perimeter of the first deck is 16, so each side of the square deck measures 16/4 = <<16/4=4>>4 units.
The area of the first deck is 4 * 4 = <<4*4=16>>16 square units.
So the area of the tile for the first deck is 16/2 = <<16/2=8>>8 square units.
For the second deck, the perimeter is 20, so each side of the square deck measures 20/4 = <<20/4=5>>5 units.
The area of the second deck is 5 * 5 = <<5*5=25>>25 square units.
So the area of the tile for the second deck is 25/2 = <<25/2=12.5>>12.5 square units.
For the third deck, the perimeter is 24, so each side of the square deck measures 24/4 = <<24/4=6>>6 units.
The area of the third deck is 6 * 6 = <<6*6=36>>36 square units.
So the area of the tile for the third deck is 36/2 = <<36/2=18>>18 square units.
For the fourth deck, the perimeter is 28, so each side of the square deck measures 28/4 = <<28/4=7>>7 units.
The area of the fourth deck is 7 * 7 = <<7*7=49>>49 square units.
So the area of the tile for the fourth deck is 49/2 = <<49/2=24.5>>24.5 square units.
Since the area of the deck increases by 9 square units each time, the area of the tile will increase by half of 9 square units each time.
So the area of the tile for the seventh deck will be 24.5 + (3 * 0.5) = 26 square units. Answer: \boxed{26}.