A box needs to be decorated to use as a prop in a play The bottom and the back do not need to be decorated what is the surface area of the box that needs to be decorated? length 27 cm width 20 cm height 20 cm

Answer 1

To determine the surface area of the box that needs to be decorated, we start with the dimensions provided: length (L) = 27 cm, width (W) = 20 cm, and height (H) = 20 cm.

The box has the following surfaces:

1. Front: 27 cm (length) × 20 cm (height)
2. Left side: 20 cm (width) × 20 cm (height)
3. Right side: 20 cm (width) × 20 cm (height)
4. Top: 27 cm (length) × 20 cm (width)

Since the bottom and back do not need to be decorated, we will calculate the surface areas of the front, left side, right side, and top.

1. Area of the front: \[ \text{Area}_{\text{front}} = L \times H = 27 , \text{cm} \times 20 , \text{cm} = 540 , \text{cm}^2 \]

2. Area of the left side: \[ \text{Area}_{\text{left}} = W \times H = 20 , \text{cm} \times 20 , \text{cm} = 400 , \text{cm}^2 \]

3. Area of the right side: \[ \text{Area}_{\text{right}} = W \times H = 20 , \text{cm} \times 20 , \text{cm} = 400 , \text{cm}^2 \]

4. Area of the top: \[ \text{Area}_{\text{top}} = L \times W = 27 , \text{cm} \times 20 , \text{cm} = 540 , \text{cm}^2 \]

Now, sum these areas to find the total surface area that needs decorating:

\[ \text{Total Surface Area} = \text{Area}{\text{front}} + \text{Area}{\text{left}} + \text{Area}{\text{right}} + \text{Area}{\text{top}} \]

\[ \text{Total Surface Area} = 540 , \text{cm}^2 + 400 , \text{cm}^2 + 400 , \text{cm}^2 + 540 , \text{cm}^2 \]

Now compute the final sum:

\[ \text{Total Surface Area} = 540 + 400 + 400 + 540 = 1880 , \text{cm}^2 \]

Thus, the surface area of the box that needs to be decorated is 1880 cm².

Answer 2

are you sure?

Answer 3

Let’s re-evaluate the calculation step by step to ensure accuracy.

The box has the following dimensions:

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

Surfaces to decorate:

• Front face
• Left face
• Right face
• Top face

1. Area of the front: \[ \text{Area}_{\text{front}} = L \times H = 27 , \text{cm} \times 20 , \text{cm} = 540 , \text{cm}^2 \]

2. Area of the left side: \[ \text{Area}_{\text{left}} = W \times H = 20 , \text{cm} \times 20 , \text{cm} = 400 , \text{cm}^2 \]

3. Area of the right side: \[ \text{Area}_{\text{right}} = W \times H = 20 , \text{cm} \times 20 , \text{cm} = 400 , \text{cm}^2 \]

4. Area of the top: \[ \text{Area}_{\text{top}} = L \times W = 27 , \text{cm} \times 20 , \text{cm} = 540 , \text{cm}^2 \]

Now, let's sum these areas:

\[ \text{Total Surface Area} = \text{Area}{\text{front}} + \text{Area}{\text{left}} + \text{Area}{\text{right}} + \text{Area}{\text{top}} \]

Calculating that:

\[ \text{Total Surface Area} = 540 , \text{cm}^2 + 400 , \text{cm}^2 + 400 , \text{cm}^2 + 540 , \text{cm}^2 \]

Adding them together:

\[ 540 + 400 + 400 + 540 = 1880 , \text{cm}^2 \]

So, I confirm my previous calculation. The surface area of the box that needs to be decorated is indeed 1880 cm². If you have further questions or want to clarify anything else, feel free to ask!