An illustration shows the unfolded version of a rectangular prism composed of 6 rectangles. There are four adjoining rectangles positioned vertically. The first and third are similar and bigger. The second and fourth are similar and smaller. The third rectangle is labeled as 6 feet on the left side. The fourth rectangle is labeled as 8 feet on the bottom side. The fourth rectangle shares the left and right sides with two similar rectangles, one on each side. The rectangle on the left is labeled as 3.5 feet on the left side.
What is the surface area of this prism?
(1 point)
Responses
194 ft.2
194 ft. squared
168 ft.2
, 168 ft. squared
97 ft.2
, 97 ft. squared
35 ft.2
, 35 ft. squared
We can start by identifying the dimensions of each rectangle based on the given labels. Let's label the rectangles as follows:
1. 6 ft x a
2. b x c
3. 6 ft x a
4. b x 8 ft
5. 6 ft x a
6. b x c
From the illustration, we can see that a = c = 8 ft (since they are opposite sides of the same rectangle) and b = 3.5 ft + 6 ft + 3.5 ft = 13 ft (since it is the sum of the lengths of the three rectangles that share its height).
Now, we can calculate the surface area of the prism by adding up the areas of each rectangle:
1. 6 ft x 8 ft = 48 ft^2
2. 13 ft x 8 ft = 104 ft^2
3. 6 ft x 8 ft = 48 ft^2
4. 13 ft x 8 ft = 104 ft^2
5. 6 ft x 8 ft = 48 ft^2
6. 13 ft x 8 ft = 104 ft^2
Total surface area = 48 ft^2 + 104 ft^2 + 48 ft^2 + 104 ft^2 + 48 ft^2 + 104 ft^2 = 456 ft^2
Therefore, the surface area of the prism is 456 ft^2.