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? Deck Perimeter First 24 feet Second 28 feet Third 32 feet Fourth 36 feet (1 point) Responses 6 square feet 6 square feet 12 square feet 12 square feet 72 square feet 72 square feet 144 square feet
The rule to find the area of the tile is to divide the area of the deck by 2.
To find the area of the tile, we need to find the area of the deck.
From the given information, we can find that the side length of the first deck is $24/4=6$ feet, the side length of the second deck is $28/4=7$ feet, the side length of the third deck is $32/4=8$ feet, and the side length of the fourth deck is $36/4=9$ feet.
Since the decks are square, the area of the deck is equal to the square of its side length.
Therefore, the area of the first deck is $6^2=36$ square feet, the area of the second deck is $7^2=49$ square feet, the area of the third deck is $8^2=64$ square feet, and the area of the fourth deck is $9^2=81$ square feet.
According to the rule, the area of the tile for the first deck is $36/2=18$ square feet, the area of the tile for the second deck is $49/2=24.5$ square feet, the area of the tile for the third deck is $64/2=32$ square feet, and the area of the tile for the fourth deck is $81/2=40.5$ square feet.
Therefore, the area of the tile for the seventh deck would be $40.5$ square feet.