To find the surface area of the box that needs to be decorated, we need to calculate the surface area of the sides and the top while excluding the bottom and back.
Assuming the box is rectangular, let’s denote the dimensions of the box as follows:
- Length (L)
- Width (W)
- Height (H)
The surface area of a rectangular box can be calculated with the formula: \[ \text{Surface Area} = 2(LW + LH + WH) \]
However, since we only want the area of the top and the four sides (excluding the bottom and back), we will calculate it as follows:
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Top surface area: \[ \text{Top} = L \times W \]
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Front surface area (one of the sides, height): \[ \text{Front} = W \times H \]
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Left surface area (one of the sides, height): \[ \text{Left} = L \times H \]
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Right surface area (one of the sides, height): \[ \text{Right} = L \times H \]
Since we have two side heights (left and right): \[ \text{Total for sides} = 2(L \times H + W \times H) = 2LH + 2WH \]
Putting it together: \[ \text{Total Surface Area to be decorated} = L \times W + 2(L \times H + W \times H) \] or \[ \text{Total Surface Area to be decorated} = L \times W + 2LH + 2WH \]
Without specific dimensions provided for L, W, and H, we cannot compute a numerical answer.
However, the provided options for responses seem to suggest that some specific dimensions have likely been used for the calculation. To select an answer, typically, one would need the dimensions or to apply the reasoning provided.
Since I have no dimensions, I cannot confirm the exact surface area to be decorated. If you can provide the dimensions of the box, I’d be glad to help calculate the surface area!