Question

steve is going to a party for nancy. he found a box for her gift, but he needs to know the surface area so he can buy wrapping paper. find the surface area, and show your work.

Explanation:

The box is a rectangular prism. The formula for the surface area \( SA \) of a rectangular prism is \( SA = 2(lw + lh + wh) \), where \( l \) is length, \( w \) is width, and \( h \) is height. From the diagram, \( l = 10.5 \) in, \( w = 1.8 \) in, \( h = 14.5 \) in.

Step 1: Calculate \( lw \), \( lh \), \( wh \)

• \( lw = 10.5 \times 1.8 = 18.9 \)
• \( lh = 10.5 \times 14.5 = 152.25 \)
• \( wh = 1.8 \times 14.5 = 26.1 \)

Step 2: Plug into the surface area formula

\( SA = 2(18.9 + 152.25 + 26.1) \)
First, add the terms inside the parentheses: \( 18.9 + 152.25 + 26.1 = 197.25 \)
Then multiply by 2: \( SA = 2 \times 197.25 = 394.5 \) square inches.

(Note: The handwritten work in the image seems to have calculation errors, so we use the correct formula for a rectangular prism's surface area.)

Answer:

The surface area of the box is \( \boldsymbol{394.5} \) square inches.