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40 votes
HELP PLS!! D:

The net of a rectangular prism is shown below. What is the total surface area of this prism?

A. 112 cm²
B. 142 cm²
C. 105 cm²
D. 71 cm²

HELP PLS!! D: The net of a rectangular prism is shown below. What is the total surface-example-1
User Bank
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1 Answer

17 votes
17 votes

Answer: 142 cm^2 (choice B)

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Step-by-step explanation:

Think of unwrapping a present and doing so without any unnecessary tearing. That means there aren't any little small pieces thrown away. There are many ways to unwrap a 3D box, and this diagram shows one of many ways. This flat layout is the 2D version of the 3D surfaces.

To find the surface area of the 3D figure, we simply need to find the area of each rectangle in this 2D flat net. Once we know all the little areas, we add them up to get the surface area.

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The lowest rectangle is 3 cm by 5 cm, so its area is 3*5 = 15 cm^2. Let A = 15 so we can use it later.

Let's move to the middle row of four rectangles. From left to right, we have these four rectangular areas

  • 3*7 = 21 cm^2
  • 5*7 = 35 cm^2
  • 3*7 = 21 cm^2
  • 5*7 = 35 cm^2

I'll call these results B,C,D,E in the order given above. So B = 21, C = 35, etc.

The rectangle up top has area of 3*5 = 15 cm^2. I'll let F = 15

Lastly, we'll add up the sub-areas to get the grand total

A+B+C+D+E+F = 15+21+35+21+35+15 = 142 cm^2 is the surface area

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Another pathway to the answer:

If you can picture how this flat diagram would fold up, then you would see that we'd get a 3D block with the following dimensions

  • L = 7 cm
  • W = 5 cm
  • H = 3 cm

The order of L,W,H doesn't really matter.

Then we can use the 3D block surface area formula like so

SA = 2*(LW + LH + WH)

SA = 2*(7*5 + 7*3 + 5*3)

SA = 2*(35 + 21 + 15)

SA = 2*71

SA = 142 cm^2 is the surface area

As you can see from the third step, we have "35", "21" and "15" show up again. The 2 out front is because we have 2 copies of each item mentioned.

User Linuts
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