Question

Blanca is going to use a box that is a rectangular prism for a card box at her son’s birthday party. She will wrap and decorate the box. The dimensions of the box are shown in the diagram.
10.5 in

7 in

9.1 in
What is the total surface area of the box in square inches?

Answer 1

To find the total surface area of a rectangular prism (box), we 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 the dimensions:
- Length \( l = 10.5 \) in
- Width \( w = 7 \) in
- Height \( h = 9.1 \) in

Now, we can plug in these values into the surface area formula:

1. Calculate each of the products:
- \( lw = 10.5 \times 7 = 73.5 \)
- \( lh = 10.5 \times 9.1 = 95.55 \)
- \( wh = 7 \times 9.1 = 63.7 \)

2. Now, sum these values:
\[
lw + lh + wh = 73.5 + 95.55 + 63.7 = 232.75
\]

3. Finally, multiply by 2 to get the total surface area:
\[
\text{Surface Area} = 2 \times 232.75 = 465.5
\]

Therefore, the total surface area of the box is \( \boxed{465.5} \) square inches.