Question

Stephen wants to wrap a present in a box for his mother. The box measures 12 cm wide, 4 cm high, 17 cm long. How much wrapping paper will Stephen need to wrap the present?

Answer 1

To determine how much wrapping paper Stephen will need, we first need to calculate the surface area of the box. The surface area \(A\) of a rectangular box can be calculated using the formula:

\[
A = 2(lw + lh + wh)
\]

where:
- \(l\) is the length,
- \(w\) is the width,
- \(h\) is the height.

In this case:
- \(l = 17 \text{ cm}\),
- \(w = 12 \text{ cm}\),
- \(h = 4 \text{ cm}\).

Now, let's calculate each product:

1. \(lw = 17 \text{ cm} \times 12 \text{ cm} = 204 \text{ cm}^2\)
2. \(lh = 17 \text{ cm} \times 4 \text{ cm} = 68 \text{ cm}^2\)
3. \(wh = 12 \text{ cm} \times 4 \text{ cm} = 48 \text{ cm}^2\)

Now, substitute these values into the surface area formula:

\[
A = 2(204 \text{ cm}^2 + 68 \text{ cm}^2 + 48 \text{ cm}^2)
\]

Calculate the sum of the areas:

\[
204 + 68 + 48 = 320 \text{ cm}^2
\]

Now, multiply this sum by 2 to find the total surface area:

\[
A = 2 \times 320 \text{ cm}^2 = 640 \text{ cm}^2
\]

Thus, the amount of wrapping paper that Stephen will need to wrap the present is:

\[
\boxed{640 \text{ cm}^2}
\]