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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its wrong
To find the lateral surface area of the rectangular prism represented by the given net, we need to calculate the area of each of the four side rectangles and add them up.
The lateral surface area is the sum of the areas of the two side rectangles and two bottom rectangles.
First, calculate the area of the side rectangles:
Area of side rectangles = 2 * height * width = 2 * 12 cm * 3 cm = 72 cm2
Next, calculate the area of the bottom rectangles:
Area of bottom rectangles = 2 * length * width = 2 * 12 cm * 7 cm = 168 cm2
Add the area of the side rectangles and the area of the bottom rectangles to find the lateral surface area:
Lateral Surface Area = 72 cm2 + 168 cm2 = 240 cm2
Therefore, the lateral surface area of the rectangular prism represented by the given net is 240 cm2.
I apologize for the mistake in my previous response. Let's correctly calculate the lateral surface area of the rectangular prism:
Since the net shows the sides, bottom, and top of the rectangular prism, we will calculate the lateral surface area by adding the areas of the side rectangles.
Given:
- The bottom rectangle has a length of 12 cm and a width of 7 cm.
- The two side rectangles have a width of 3 cm each.
Area of the bottom rectangle = length * width = 12 cm * 7 cm = 84 cm^2
Area of each side rectangle = length * height = 12 cm * 3 cm = 36 cm^2
Since there are two side rectangles, the total area of the side rectangles = 2 * 36 cm^2 = 72 cm^2
Lateral Surface Area = Total area of the side rectangles = 72 cm^2
Therefore, the correct lateral surface area of the rectangular prism represented by the given net is 72 cm^2.