Question

Use the image to answer the question. A box needs to be decorated to use as a prop in a play. The bottom and the back of the box do not need to be decorated. What is the surface area of the box that needs to be decorated? (1 point)

Answer 1

To calculate the surface area that needs to be decorated on a box, we should first identify which surfaces are involved. Given that the bottom and back do not need to be decorated, we only need to consider the following surfaces:

1. **Top** of the box
2. **Front** of the box
3. **Left Side** of the box
4. **Right Side** of the box

Let’s denote the dimensions of the box as:
- Length (L)
- Width (W)
- Height (H)

The surface areas of the individual sides can be calculated as follows:

- **Top Surface Area**: \( L \times W \)
- **Front Surface Area**: \( W \times H \)
- **Left Side Surface Area**: \( L \times H \)
- **Right Side Surface Area**: \( L \times H \)

Now, calculating the total surface area that needs to be decorated:

\[
\text{Total Surface Area} = \text{Top Surface Area} + \text{Front Surface Area} + \text{Left Side Surface Area} + \text{Right Side Surface Area}
\]

\[
= (L \times W) + (W \times H) + (L \times H) + (L \times H)
\]

\[
= L \times W + W \times H + 2 \times (L \times H)
\]

This formula gives you the total surface area for the parts of the box that need to be decorated. To find the exact value, substitute the actual dimensions for L, W, and H into the equation. If you provide the dimensions, I can help with the precise calculation.