Use the image to answer the 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

222 square inches
222 square inches

180 square inches
180 square inches

270 square inches
270 square inches

111 square inches
]

1 answer

To find the surface area of a rectangular prism, use the formula:

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

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

Given:

  • Length (\( l \)) = 12 inches
  • Width (\( w \)) = 5 inches
  • Height (\( h \)) = 3 inches

Now plug the values into the formula:

  1. Calculate the area of each pair of opposite faces:

    • \( lw = 12 \times 5 = 60 \)
    • \( lh = 12 \times 3 = 36 \)
    • \( wh = 5 \times 3 = 15 \)
  2. Add these areas together: \[ lw + lh + wh = 60 + 36 + 15 = 111 \]

  3. Multiply the sum by 2 to get the total surface area: \[ \text{Surface Area} = 2 \times 111 = 222 \text{ square inches} \]

Thus, the surface area of the rectangular prism is 222 square inches. The correct response is:

222 square inches.