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
138 cm.2
138 cm.2
306 cm.2
306 cm.2
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To find the surface area of the rectangular prism, we need to find the area of each face and add them up.
1. The front face has a length of 7 cm and a width of 2 cm, so its area is 7 * 2 = 14 cm^2.
2. The back face is the same size as the front face, so its area is also 14 cm^2.
3. The top face has a length of 7 cm and a width of 10 cm, so its area is 7 * 10 = 70 cm^2.
4. The bottom face is the same size as the top face, so its area is also 70 cm^2.
5. The two side faces are the same size and are the same size as the front and back faces, so their combined area is 2 * (14 + 70) = 168 cm^2.
Now, add up all the face areas:
14 + 14 + 70 + 70 + 168 = 336
Therefore, the surface area of the rectangular prism is 336 cm^2.
wrong
My apologies for the mistake. Let's correct it.
1. The front face has a length of 7 cm and a width of 2 cm, so its area is 7 * 2 = 14 cm^2.
2. The back face is the same size as the front face, so its area is also 14 cm^2.
3. The top face has a length of 7 cm and a width of 10 cm, so its area is 7 * 10 = 70 cm^2.
4. The bottom face is the same size as the top face, so its area is also 70 cm^2.
5. The two side faces are the same size and have dimensions 10 cm by 7 cm, so their combined area is 2 * (10 * 7) = 140 cm^2.
Now, add up all the face areas:
14 + 14 + 70 + 70 + 140 = 308
Therefore, the surface area of the rectangular prism is 308 cm^2.
still wrong
Let's correct it once more:
1. Front and back faces: 2 faces, each with an area of 7 cm x 10 cm = 70 cm^2
2. Top and bottom faces: 2 faces, each with an area of 7 cm x 2 cm = 14 cm^2
3. Left and right side faces: 2 faces, each with an area of 10 cm x 2 cm = 20 cm^2
Now, add up all the face areas:
70 + 70 + 14 + 14 + 20 + 20 = 208
Therefore, the surface area of the rectangular prism is 208 cm^2.