Surface Area of Rectangular Prisms Quick Check

Question

5 of 55 of 5 Items

Question
Use the image to answer the 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 find the surface area of a rectangular prism, you need to find the areas of all six rectangles that make up the prism's surfaces and then sum these areas up.

Here we are given an unfolded view (a net) of the prism with the following dimensions:

- 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 left side of the rectangle that shares the side with another is labeled as 3.5 feet.

First, identify and list out the dimensions for all three distinct pairs of rectangles:

1. The dimensions of the third and fourth larger rectangles:
- Length: 6 feet
- Width: 8 feet

The area of each is:
\[ \text{Area} = 6 \text{ ft} \times 8 \text{ ft} = 48 \text{ ft}^2 \]
Since there are two of these:
\[ 2 \times 48 \text{ ft}^2 = 96 \text{ ft}^2 \]

2. The dimensions of the first and third medium rectangles:
- Length: 6 feet
- Width: 3.5 feet

The area of each is:
\[ \text{Area} = 6 \text{ ft} \times 3.5 \text{ ft} = 21 \text{ ft}^2 \]
Since there are two of these:
\[ 2 \times 21 \text{ ft}^2 = 42 \text{ ft}^2 \]

3. The dimensions of the second and the corresponding rectangles which adjoin vertically:
- Length: 3.5 feet
- Width: 8 feet

The area of each is:
\[ \text{Area} = 3.5 \text{ ft} \times 8 \text{ ft} = 28 \text{ ft}^2 \]
Since there are two of these:
\[ 2 \times 28 \text{ ft}^2 = 56 \text{ ft}^2 \]

Add up the areas of all the rectangles to get the total surface area of the rectangular prism:
\[ \text{Total Surface Area} = 96 \text{ ft}^2 + 42 \text{ ft}^2 + 56 \text{ ft}^2 = 194 \text{ ft}^2 \]

Therefore, the surface area of the prism is:

\[ \boxed{194 \text{ ft}^2} \]

So the correct response is:
194 ft. squared