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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
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1 answer

To determine how much wrapping paper Jerry will need to wrap the present, we need to calculate the surface area of the rectangular prism (the box).

The formula for the surface area \( S \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is:

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

Given:

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

Now, substituting the values into the formula:

  1. Calculate \( 2lw \): \[ 2lw = 2 \times 17 \times 10 = 340 \text{ cm}^2 \]

  2. Calculate \( 2lh \): \[ 2lh = 2 \times 17 \times 4 = 136 \text{ cm}^2 \]

  3. Calculate \( 2wh \): \[ 2wh = 2 \times 10 \times 4 = 80 \text{ cm}^2 \]

Now, add these areas together to get the total surface area:

\[ S = 340 + 136 + 80 \] \[ S = 556 \text{ cm}^2 \]

Thus, the surface area of the box, and the amount of wrapping paper Jerry will need, is:

\[ \text{surface area} = 556 \text{ cm}^2 \]