What is the surface area of a rectangular prism with a length of 16 inches, a height of 4 inches, and a width of 8 inches? (1 point) 224 square inches 192 square inches 448 square inches 256 square inches

1 answer

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

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

where:

  • \( l \) is the length,
  • \( w \) is the width,
  • \( h \) is the height.

Given the dimensions:

  • Length \( l = 16 \) inches,
  • Width \( w = 8 \) inches,
  • Height \( h = 4 \) inches.

First, calculate the areas of the three pairs of faces:

  1. \( lw = 16 \times 8 = 128 \) square inches
  2. \( lh = 16 \times 4 = 64 \) square inches
  3. \( wh = 8 \times 4 = 32 \) square inches

Next, sum these areas:

\[ lw + lh + wh = 128 + 64 + 32 = 224 \text{ square inches} \]

Now, substitute this sum into the surface area formula:

\[ S = 2(224) = 448 \text{ square inches} \]

Thus, the surface area of the rectangular prism is \( \boxed{448} \) square inches.