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Question

An illustration shows a 3 D box with length of 27 centimeters labeled as front, a width of 20 centimeters, and height of 20 centimeters.

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)
Responses

67 cm2
67 cm squared

1,080 cm
1,080 cm

2,960 cm2
2,960 cm squared

1,880 cm2
1,880 cm squared
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Answer 1

To find the surface area of the box that needs to be decorated, we need to calculate the area of the surfaces that will be decorated. Since the bottom and the back of the box do not need to be decorated, we will only include the front, both sides, and the top in our calculation.

The dimensions of the box are:

• Length (front) = 27 cm
• Width = 20 cm
• Height = 20 cm

1. Calculate the area of the front:
   Area_front = Length × Height
   Area_front = 27 cm × 20 cm = 540 cm²

2. Calculate the area of the two sides:
   Area_side = Width × Height
   Area_side = 20 cm × 20 cm = 400 cm²
   Since there are two sides, we multiply by 2:
   Area_sides = 2 × 400 cm² = 800 cm²

3. Calculate the area of the top:
   Area_top = Length × Width
   Area_top = 27 cm × 20 cm = 540 cm²

4. Total area to be decorated:
   Total_area = Area_front + Area_sides + Area_top
   Total_area = 540 cm² + 800 cm² + 540 cm² = 1,880 cm²

Thus, the surface area of the box that needs to be decorated is 1,880 cm².

Final Answer: 1,880 cm²