Use the formula for the surface area of a right rectangular prism to find the surface area of a shape with the following measurements: length = 4.5 cm width = 3.5 cm, and height = 2.5 cm.

Question

1. 10.5 cm2
2. 71.5 cm2
3. 35.75 cm2
4. 63 cm2

Answer 1

To find the surface area of a right rectangular prism, you can use the formula:

\[ \text{Surface Area} = 2(lw + lh + wh) \]

where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Given:

• Length (\( l \)) = 4.5 cm
• Width (\( w \)) = 3.5 cm
• Height (\( h \)) = 2.5 cm

Now, calculate each term:

1. \( lw = 4.5 , \text{cm} \times 3.5 , \text{cm} = 15.75 , \text{cm}^2 \)
2. \( lh = 4.5 , \text{cm} \times 2.5 , \text{cm} = 11.25 , \text{cm}^2 \)
3. \( wh = 3.5 , \text{cm} \times 2.5 , \text{cm} = 8.75 , \text{cm}^2 \)

Now, substitute these values into the formula:

\[ \text{Surface Area} = 2(15.75 + 11.25 + 8.75) \]

First, calculate the sum inside the parentheses:

\[ 15.75 + 11.25 + 8.75 = 35.75 \]

Now multiply by 2:

\[ \text{Surface Area} = 2 \times 35.75 = 71.5 , \text{cm}^2 \]

Thus, the surface area of the right rectangular prism is 71.5 cm².

The correct answer from the options provided is 2. 71.5 cm².