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An illustration shows a rectangular prism with its length measuring 17 centimeters, width measuring 10 centimeters, and height measuring 4 centimeters. The edges that are not visible are marked as dashed lines.

Jerry wants to wrap a present in a box for his mother. The box measures 10 cm wide, 4 cm high, and 17 cm long. How much wrapping paper will Jerry need to wrap the present?

(1 point)
surface area=

cm2

1 answer

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

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

where:

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

For the box Jerry is wrapping, the dimensions are:

  • Length (\( l \)) = 17 cm
  • Width (\( w \)) = 10 cm
  • Height (\( h \)) = 4 cm

Now, plug in the dimensions into the formula:

  1. Calculate \( lw \): \[ lw = 17 , \text{cm} \times 10 , \text{cm} = 170 , \text{cm}^2 \]

  2. Calculate \( lh \): \[ lh = 17 , \text{cm} \times 4 , \text{cm} = 68 , \text{cm}^2 \]

  3. Calculate \( wh \): \[ wh = 10 , \text{cm} \times 4 , \text{cm} = 40 , \text{cm}^2 \]

Now, sum these areas: \[ lw + lh + wh = 170 , \text{cm}^2 + 68 , \text{cm}^2 + 40 , \text{cm}^2 = 278 , \text{cm}^2 \]

Finally, multiply by 2 to find the total surface area: \[ \text{Surface Area} = 2 \times 278 , \text{cm}^2 = 556 , \text{cm}^2 \]

Thus, the surface area of the box is: \[ \text{Surface Area} = 556 , \text{cm}^2 \]

So, Jerry will need 556 cm² of wrapping paper to wrap the present.