Question

An illustration shows a rectangular prism with length 12 inches, width 5 inches, and height 3 inches. The top, front, and right faces are visible. The edges that are not visible are represented by dashed lines.
Solve for the surface area of the rectangular prism.

(1 point)
Responses

111 square inches
111 square inches

180 square inches
180 square inches

222 square inches
222 square inches

270 square inches

Answer 1

To calculate the surface area of a rectangular prism, we can use the formula:

\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]

where:
- \( l \) = length
- \( w \) = width
- \( h \) = height

For this rectangular prism, the dimensions are:
- Length (\( l \)) = 12 inches
- Width (\( w \)) = 5 inches
- Height (\( h \)) = 3 inches

Now, let's plug in the values into the formula:

1. Calculate \( 2lw \):
\[
2lw = 2 \times 12 \times 5 = 120 \text{ square inches}
\]

2. Calculate \( 2lh \):
\[
2lh = 2 \times 12 \times 3 = 72 \text{ square inches}
\]

3. Calculate \( 2wh \):
\[
2wh = 2 \times 5 \times 3 = 30 \text{ square inches}
\]

Now, add these areas together:

\[
\text{Surface Area} = 120 + 72 + 30 = 222 \text{ square inches}
\]

Therefore, the surface area of the rectangular prism is **222 square inches**.