What is the surface area of a rectangular prism whose dimensions are 334 dm×412 dm×5 dm in square decimeters?(1 point) Responses 116 1/4 dm2 116 dm squared 84 3/8 dm2 84 58 1/8 8 dm2 58 16 dm2

Answer 1

To calculate the surface area \( S \) of a rectangular prism, you can use the formula:

\[ S = 2(lw + lh + wh) \]

where \( l \), \( w \), and \( h \) are the length, width, and height of the prism.

Given the dimensions:

• \( l = 334 \) dm
• \( w = 412 \) dm
• \( h = 5 \) dm

First, we calculate each of the products:

1. \( lw = 334 \times 412 \)
2. \( lh = 334 \times 5 \)
3. \( wh = 412 \times 5 \)

Now, let's calculate these values:

1. \( lw = 334 \times 412 = 137048 \)
2. \( lh = 334 \times 5 = 1670 \)
3. \( wh = 412 \times 5 = 2060 \)

Now, sum these products:

\[ lw + lh + wh = 137048 + 1670 + 2060 = 139778 \]

Now multiply by 2 to find the surface area:

\[ S = 2 \times 139778 = 279556 \text{ dm}^2 \]

So, the surface area of the rectangular prism is \( 279556 \) dm².

However, since that does not match any of the response options, verify that all steps are consistent—calculations seem correct but recheck available options. None seem to reflect this large area. It may be worth checking the context or provided answers again based on this derived calculation.