Question

diagram of a toy box is shown. Its measurements are given in inches.

Height 30 in
Length 34 in
Width 40 in

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

Answer 1

To calculate the total surface area of a rectangular box (or cuboid), you can use the formula:

\[
\text{Surface Area} = 2(Length \times Width + Length \times Height + Width \times Height)
\]

Given the measurements of the toy box:
- Height (H) = 30 inches
- Length (L) = 34 inches
- Width (W) = 40 inches

Now, we can substitute these values into the formula:

1. Calculate each product:
- Length × Width = \(34 \, \text{in} \times 40 \, \text{in} = 1360 \, \text{in}^2\)
- Length × Height = \(34 \, \text{in} \times 30 \, \text{in} = 1020 \, \text{in}^2\)
- Width × Height = \(40 \, \text{in} \times 30 \, \text{in} = 1200 \, \text{in}^2\)

2. Now, sum these areas:
\[
1360 + 1020 + 1200 = 3580 \, \text{in}^2
\]

3. Finally, multiply by 2 to get the total surface area:
\[
\text{Surface Area} = 2 \times 3580 = 7160 \, \text{in}^2
\]

Thus, the total surface area of the toy box is \( \boxed{7160} \) square inches.