Question

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)
Responses

224 square inches
224 square inches

448 square inches
448 square inches

192 square inches
192 square inches

256 square inches

Answer 1

The surface area \( S \) of a rectangular prism can be calculated using the formula:

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

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

Given:
- Length \( l = 16 \) inches
- Width \( w = 8 \) inches
- Height \( h = 4 \) inches

Substituting the values into the formula:

\[
S = 2(16 \cdot 8 + 16 \cdot 4 + 8 \cdot 4)
\]

Calculating each term:
- \( 16 \cdot 8 = 128 \)
- \( 16 \cdot 4 = 64 \)
- \( 8 \cdot 4 = 32 \)

Now, summing these results:

\[
128 + 64 + 32 = 224
\]

Now, substituting back into the surface area formula:

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

Thus, the surface area of the rectangular prism is **448 square inches**.