Question

Surface Area of Right Rectangular Prisms Quick Check
5 of 55 of 5 Items
Question
Use the image to answer the 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

1,880 cm2
1,880 cm squared

67 cm2
67 cm squared

2,960 cm2
2,960 cm squared

1,080 cm

Answer 1

To find the surface area of the box that needs to be decorated, we need to calculate the surface area of each face that will be decorated and then sum those areas.

Given dimensions:
- Length (l) = 27 cm
- Width (w) = 20 cm
- Height (h) = 20 cm

Since the bottom and back of the box do not need to be decorated, we only need to calculate the area of the front, two sides, and the top:

1. **Front face** (area = height × width) = 20 cm × 27 cm = 540 cm²
2. **Back face** (not decorated, so do not include)
3. **Left side face** (area = height × length) = 20 cm × 20 cm = 400 cm²
4. **Right side face** (area = height × length) = 20 cm × 20 cm = 400 cm²
5. **Top face** (area = length × width) = 27 cm × 20 cm = 540 cm²
6. **Bottom face** (not decorated, so do not include)

Now sum the areas of the faces that need to be decorated:

Total surface area to be decorated = Front + Left Side + Right Side + Top

= 540 cm² (Front) + 400 cm² (Left) + 400 cm² (Right) + 540 cm² (Top)

= 540 + 400 + 400 + 540 = 1880 cm²

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