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
138 cm.2
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306 cm^2
To find the surface area of the rectangular prism, we need to calculate the area of each of the six faces and then add them together.
The dimensions of the rectangular prism can be determined from the net shown in the image:
- The front and back faces are the first and second rectangles with measurements 7 cm x 2 cm and 7 cm x 4 cm respectively. Their total area is 7 cm x 2 cm + 7 cm x 4 cm = 14 cm^2 + 28 cm^2 = 42 cm^2.
- The top and bottom faces are the second and fourth rectangles with measurements 7 cm x 4 cm and 10 cm x 4 cm respectively. Their total area is 28 cm^2 + 40 cm^2 = 68 cm^2.
- The left and right faces are identical, with measurements 10 cm x 2 cm each. Their total area is 20 cm^2 + 20 cm^2 = 40 cm^2.
Adding up the area of all six faces gives us: 42 cm^2 + 68 cm^2 + 40 cm^2 = 150 cm^2.
Therefore, the surface area of the rectangular prism is 150 cm^2 x 2 = 300 cm^2.