Use the image to answer the question.

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

2,960 cm2
2,960 cm squared

1,880 cm2
1,880 cm squared

1,080 cm

Answer 1

To find the surface area that needs to be decorated (the front, two sides, and top of the box), we can calculate it as follows:

1. Dimensions of the box:

   • Length (L) = 27 cm
   • Width (W) = 20 cm
   • Height (H) = 20 cm

2. Surface area to be decorated:

   • Front face: Length × Height = \( 27 \text{ cm} \times 20 \text{ cm} = 540 \text{ cm}^2 \)
   • Top face: Length × Width = \( 27 \text{ cm} \times 20 \text{ cm} = 540 \text{ cm}^2 \)
   • Two side faces: Width × Height for each side = \( 20 \text{ cm} \times 20 \text{ cm} = 400 \text{ cm}^2 \) (for one side)
     Therefore, for two sides: \( 400 \text{ cm}^2 \times 2 = 800 \text{ cm}^2 \)

3. Total surface area to decorate:

   • Combine all the areas calculated: \[ \text{Total area} = \text{Front} + \text{Top} + 2 \times \text{Side} \] \[ \text{Total area} = 540 \text{ cm}^2 + 540 \text{ cm}^2 + 800 \text{ cm}^2 = 1880 \text{ cm}^2 \]

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