Question

the 1st deck is 24ft the 2nd deck is 28ft the 3rd deck is 32ft and the 4th deck is 36ft. the rule is to divied by 2. whats the area for the 7th deck? the decks are square and the deck are in the center of the room. The answer choises are 6sq ft, 12sq ft, 72 sq ft, and 144 sq ft

Answer 1

To find the area of the 7th deck, we can use the rule given to us:

For each successive deck, the length doubles.

The length of the 1st deck is 24 ft.
Thus, the length of the 2nd deck is 24 ft / 2 = 12 ft.
The length of the 3rd deck is 12 ft / 2 = 6 ft.
The length of the 4th deck is 6 ft / 2 = 3 ft.

Therefore, we can see a pattern:

1st deck: 24 ft
2nd deck: 12 ft
3rd deck: 6 ft
4th deck: 3 ft

We can assume that the length of the 5th deck would be 3 ft / 2 = 1.5 ft, the length of the 6th deck would be 1.5 ft / 2 = 0.75 ft, and the length of the 7th deck would be 0.75 ft / 2 = 0.375 ft.

Since the decks are square, to find the area of each deck, we square their length.

The area of the 1st deck: 24 ft * 24 ft = 576 sq ft
The area of the 2nd deck: 12 ft * 12 ft = 144 sq ft
The area of the 3rd deck: 6 ft * 6 ft = 36 sq ft
The area of the 4th deck: 3 ft * 3 ft = 9 sq ft
The area of the 5th deck: 1.5 ft * 1.5 ft = 2.25 sq ft
The area of the 6th deck: 0.75 ft * 0.75 ft = 0.5625 sq ft
The area of the 7th deck: 0.375 ft * 0.375 ft = 0.140625 sq ft

So, the area of the 7th deck is 0.140625 sq ft.