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.

Question

(The image features a rectangular shape. The dimensions of the rectangle are 9.1 inches in length and 7 inches in width, with an additional measurement of 10.5 inches that may refer to height or another relevant dimension. The diagram likely includes lines or plots showing angles, possibly relating to origami design techniques, emphasizing geometry and structure within the context provided by the tags.)
What is the total surface area of the box in square inches?

Answer 1

To find the total surface area of a rectangular prism (in this case, a box), we use the formula for the surface area, which is given by:

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

where:

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

From your description, the dimensions of the box are:

• Length (\(l\)) = 9.1 inches
• Width (\(w\)) = 7 inches
• Height (\(h\)) = 10.5 inches

Now substituting the values into the formula:

1. Calculate \(2lw\): \[ 2lw = 2 \times 9.1 \times 7 = 2 \times 63.7 = 127.4 \text{ square inches} \]

2. Calculate \(2lh\): \[ 2lh = 2 \times 9.1 \times 10.5 = 2 \times 95.55 = 191.1 \text{ square inches} \]

3. Calculate \(2wh\): \[ 2wh = 2 \times 7 \times 10.5 = 2 \times 73.5 = 147 \text{ square inches} \]

Now, sum these areas to find the total surface area:

\[ SA = 127.4 + 191.1 + 147 = 465.5 \text{ square inches} \]

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