Use the image to answer the question.
An illustration shows an unfolded version of a rectangular prism.
A large vertical rectangle is divided into four stacked horizontal rectangles labeled as side, bottom, side, and top, all with common dashed lines in between them. The second rectangle, labeled as bottom, shows a length of 12 centimeters and a width of 7 centimeters. There are two additional rectangles adjoined to both sides of the second rectangle, with common dashed lines in between them. These two adjoined rectangles are labeled as side, each with a width of 3 centimeters.
Find the lateral surface area of the rectangular prism represented by the given net.
(1 point)
cm2
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The lateral surface area of a rectangular prism is calculated by adding up the areas of the four side rectangles.
The top and bottom rectangles have dimensions of 12 cm x 7 cm each, so their areas would be 12 cm x 7 cm = 84 cm^2 each.
The two side rectangles have dimensions of 12 cm x 3 cm each, so their areas would be 12 cm x 3 cm = 36 cm^2 each.
Therefore, the lateral surface area of the rectangular prism represented by the given net would be: 84 cm^2 + 84 cm^2 + 36 cm^2 + 36 cm^2 = 240 cm^2.
So, the lateral surface area of the rectangular prism is 240 cm^2.
bot noo
I apologize for the mistake. Let's recalculate the lateral surface area of the rectangular prism represented by the given net.
Each long side of the rectangle prism has dimensions of 12 cm x 7 cm. These are the top and bottom rectangles in the unfolded version. So, the area of each of these rectangles is 12 cm x 7 cm = 84 cm^2.
The two shorter sides of the prism have dimensions of 7 cm x 3 cm each. These are the side rectangles in the unfolded version. So, the area of each of these rectangles is 7 cm x 3 cm = 21 cm^2.
The lateral surface area of the rectangular prism would be the sum of the areas of the two sides, which are the short sides, so:
2 x 21 cm^2 = 42 cm^2.
Therefore, the lateral surface area of the rectangular prism represented by the given net is 42 cm^2. Thank you for catching that mistake.
ummm bot um noooo
I apologize for the mistake in my previous responses. Let's correctly calculate the lateral surface area of the rectangular prism represented by the given net.
In the illustration, the dimensions are as follows:
- The bottom rectangle: 12 cm x 7 cm.
- The two side rectangles: 12 cm x 3 cm each.
The lateral surface area of a rectangular prism is found by adding the areas of the four side rectangles.
Area of the bottom rectangle= 12 cm x 7 cm = 84 cm^2
Area of each side rectangle= 12 cm x 3 cm = 36 cm^2 (there are two of these)
Total lateral surface area = 2(side rectangles ) + 2(bottom rectangle)
Total lateral surface area = 2(36 cm^2) + 2(84 cm^2)
Total lateral surface area = 72 cm^2 + 168 cm^2
Total lateral surface area = 240 cm^2
Therefore, the lateral surface area of the rectangular prism represented by the given net is 240 cm^2. Thank you for your patience.
ummm no you made a mistake
i keep on telling you know but you don't listen
My apologies for the errors in my previous responses. Let's reevaluate the lateral surface area of the rectangular prism represented by the given net.
The bottom rectangle has dimensions of 12 cm x 7 cm, so its area is 12 cm x 7 cm = 84 cm^2.
There are two side rectangles, each with dimensions of 12 cm x 3 cm. The area of each side rectangle is 12 cm x 3 cm = 36 cm^2.
The lateral surface area is the sum of the areas of the two side rectangles and the bottom rectangle:
2(side rectangles) + 2(bottom rectangle)
2(36 cm^2) + 2(84 cm^2)
72 cm^2 + 168 cm^2
= 240 cm^2
Therefore, the correct lateral surface area of the rectangular prism represented by the given net is 240 cm^2. Thank you for your patience.