Question
Question
Use the image to answer the question.
There are four adjoining rectangles of the same height positioned so their vertical sides touch. The first and third rectangles from the left are the same size as each other. The second and fourth rectangles from the left are also the same size as each other but wider than the first and third. The first rectangle is labeled 7 centimeters on the left side and 2 centimeters on the bottom side. The fourth rectangle is labeled 10 centimeters on the bottom side. The second rectangle has identical small rectangles touching its top and bottom sides. The small rectangles are the same width as the second rectangle.
The net of a rectangular prism is shown. What is the surface area of the rectangular prism?
(1 point)
Responses
104 cm.2
104 cm.2
208 cm.2
208 cm.2
306 cm.2
306 cm.2
138 cm.2
Use the image to answer the question.
There are four adjoining rectangles of the same height positioned so their vertical sides touch. The first and third rectangles from the left are the same size as each other. The second and fourth rectangles from the left are also the same size as each other but wider than the first and third. The first rectangle is labeled 7 centimeters on the left side and 2 centimeters on the bottom side. The fourth rectangle is labeled 10 centimeters on the bottom side. The second rectangle has identical small rectangles touching its top and bottom sides. The small rectangles are the same width as the second rectangle.
The net of a rectangular prism is shown. What is the surface area of the rectangular prism?
(1 point)
Responses
104 cm.2
104 cm.2
208 cm.2
208 cm.2
306 cm.2
306 cm.2
138 cm.2
Answers
Answered by
GPT-4o mini
To find the surface area of the rectangular prism based on the given dimensions, we need to identify the height, width, and length of the prism.
From the description:
- The first rectangle (7 cm height and 2 cm width) is likely a side of the prism.
- The second rectangle (height same as the first, width not specified) corresponds to the wider rectangles.
- The fourth rectangle has a bottom length of 10 cm.
Since the first rectangle is 2 cm wide, this width (2 cm) is probably matched by the third rectangle.
Assuming the base of the rectangular prism is composed of the first and the second rectangles and using the information given:
- The height of the prism = 7 cm
- Width of the base = 2 cm (first and third rectangles)
- Length of the base = 10 cm (fourth rectangle)
The surface area \( SA \) of a rectangular prism can be calculated using the formula:
\[ SA = 2lw + 2lh + 2wh \]
where \( l \) = length, \( w \) = width, and \( h \) = height.
Substituting the values:
- \( l = 10 \, \text{cm} \)
- \( w = 2 \, \text{cm} \)
- \( h = 7 \, \text{cm} \)
Calculating the surface area:
\[
SA = 2(10)(2) + 2(10)(7) + 2(2)(7)
\]
\[
= 2(20) + 2(70) + 2(14)
\]
\[
= 40 + 140 + 28
\]
\[
= 208 \, \text{cm}^2
\]
Thus, the surface area of the rectangular prism is \( 208 \, \text{cm}^2 \).
So, the correct response is:
**208 cm²**
From the description:
- The first rectangle (7 cm height and 2 cm width) is likely a side of the prism.
- The second rectangle (height same as the first, width not specified) corresponds to the wider rectangles.
- The fourth rectangle has a bottom length of 10 cm.
Since the first rectangle is 2 cm wide, this width (2 cm) is probably matched by the third rectangle.
Assuming the base of the rectangular prism is composed of the first and the second rectangles and using the information given:
- The height of the prism = 7 cm
- Width of the base = 2 cm (first and third rectangles)
- Length of the base = 10 cm (fourth rectangle)
The surface area \( SA \) of a rectangular prism can be calculated using the formula:
\[ SA = 2lw + 2lh + 2wh \]
where \( l \) = length, \( w \) = width, and \( h \) = height.
Substituting the values:
- \( l = 10 \, \text{cm} \)
- \( w = 2 \, \text{cm} \)
- \( h = 7 \, \text{cm} \)
Calculating the surface area:
\[
SA = 2(10)(2) + 2(10)(7) + 2(2)(7)
\]
\[
= 2(20) + 2(70) + 2(14)
\]
\[
= 40 + 140 + 28
\]
\[
= 208 \, \text{cm}^2
\]
Thus, the surface area of the rectangular prism is \( 208 \, \text{cm}^2 \).
So, the correct response is:
**208 cm²**