To find the surface area that needs to be decorated, we need to calculate the surface area of the parts of the box that will be decorated. The box has the following dimensions:
- Length (l) = 27 cm
- Width (w) = 20 cm
- Height (h) = 20 cm
Since the bottom and the back do not need to be decorated, we will decorate the following surfaces:
- Front (height × width)
- Two sides (height × length each)
- Top (length × width)
Step 1: Calculate the area of each part
-
Front: \[ \text{Area}_{\text{front}} = h \times w = 20 , \text{cm} \times 20 , \text{cm} = 400 , \text{cm}^2 \]
-
Two sides: \[ \text{Area}_{\text{sides}} = 2 \times (h \times l) = 2 \times (20 , \text{cm} \times 27 , \text{cm}) = 2 \times 540 , \text{cm}^2 = 1,080 , \text{cm}^2 \]
-
Top: \[ \text{Area}_{\text{top}} = l \times w = 27 , \text{cm} \times 20 , \text{cm} = 540 , \text{cm}^2 \]
Step 2: Add the areas together
Now, we add these areas to find the total surface area that needs to be decorated: \[ \text{Total area} = \text{Area}{\text{front}} + \text{Area}{\text{sides}} + \text{Area}_{\text{top}} \] \[ \text{Total area} = 400 , \text{cm}^2 + 1,080 , \text{cm}^2 + 540 , \text{cm}^2 = 2,020 , \text{cm}^2 \]
It seems I need to check again the choices given in your question because the calculated result is 2,020 cm², which does not match.
Assistance in solution:
Please ensure that the question and choices provided are as intended. In the response options you provided, none of them match the calculated area which should be 2,020 cm². The closest options seem to indicate possibly wrong figures or perhaps misinterpretation of dimensions.
If there's another property or more information from the illustration that may lead to a discrepancy, please provide that for correct estimations.