Use the image to answer the question.

Question

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

35 ft.2
35 ft. squared

168 ft.2
168 ft. squared

97 ft.2

Answer 1

To determine the surface area of the rectangular prism, let's first identify the dimensions of each face of the prism based on the description provided.

1. **Identifying the faces:**
- There are four rectangles in a vertical row: the 1st, 2nd, 3rd, and 4th rectangles.
- The 1st and 3rd rectangles are similar and bigger.
- The 2nd and 4th rectangles are similar and smaller.

2. **Known dimensions:**
- The left side of the 3rd rectangle is labeled as 6 feet.
- The bottom side of the 4th rectangle is labeled as 8 feet.
- The left side of the rectangle to the left of the 4th rectangle (one of two similar rectangles adjoining the 4th) is labeled as 3.5 feet.

From this information, we can deduce that:
- The height (h) of the prism is 6 feet (from the third rectangle).
- The width (w) of the prism is 3.5 feet (from the left side of the adjacent rectangle).
- The length (l) of the prism is 8 feet (from the bottom side of the fourth rectangle).

3. **Calculating the areas of each face:**
- Two larger rectangle faces (front and back):
- Area = height × length = 6 feet × 8 feet = 48 sq. feet each.
- Two smaller rectangle faces (top and bottom):
- Area = width × length = 3.5 feet × 8 feet = 28 sq. feet each.
- Two side rectangle faces:
- Area = height × width = 6 feet × 3.5 feet = 21 sq. feet each.

4. **Calculating the total surface area:**
- Combine the areas of all six faces:
- Total surface area = 2 (48 sq. feet) + 2 (28 sq. feet) + 2 (21 sq. feet)
- Total surface area = 96 sq. feet + 56 sq. feet + 42 sq. feet
- Total surface area = 194 sq. feet

Therefore, the surface area of the rectangular prism is **194 sq. feet**.

So, the correct answer is:
**194 ft. squared**.