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?
To find the area of the tile for the seventh deck, we first need to determine the length of each side of the deck.
Looking at the table, we can see that the perimeter of the first deck is 4, meaning each side of the deck has a length of 1.
For the second deck, the perimeter is 8, so each side has a length of 2.
For the third deck, the perimeter is 12, so each side has a length of 3.
For the fourth deck, the perimeter is 16, so each side has a length of 4.
From this pattern, we can deduce that the perimeter of the seventh deck would be 28, and thus each side would have a length of 7.
The area of a square is given by the formula A = s^2, where A is the area and s is the length of each side.
Therefore, the area of the tile for the seventh deck would be (7^2) / 2 = 49 / 2 = <<49/2=24.5>>24.5 square units. Answer: \boxed{24.5}.