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

1,080 cm
1,080 cm

1,880 cm2

Answer 1

To calculate the surface area of the box that needs to be decorated (the front, two sides, and the top), we will first find the areas of each relevant section.

1. Front Face Area:

   • Length × Height = 27 cm × 20 cm = 540 cm².

2. Top Face Area:

   • Length × Width = 27 cm × 20 cm = 540 cm².

3. Left Face Area:

   • Width × Height = 20 cm × 20 cm = 400 cm².

4. Right Face Area (identical to the Left Face):

   • Width × Height = 20 cm × 20 cm = 400 cm².

Now, we will add the areas of these sections together to get the total surface area that needs to be decorated:

• Total Area = Front Face + Top Face + Left Face + Right Face
• Total Area = 540 cm² + 540 cm² + 400 cm² + 400 cm²
• Total Area = 540 + 540 + 400 + 400 = 1,880 cm².

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