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

71.5 cm^2
35.75 cm^2
63 cm^2
10.5 cm^2

3 answers

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

First, calculate each of the products:

  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 add these values together: \[ lw + lh + wh = 15.75 , \text{cm}^2 + 11.25 , \text{cm}^2 + 8.75 , \text{cm}^2 = 35.75 , \text{cm}^2 \]

Now, multiply by 2 to find the surface area: \[ \text{Surface Area} = 2 \times 35.75 , \text{cm}^2 = 71.5 , \text{cm}^2 \]

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

you sure?

Yes, I can confirm the calculation step by step to ensure accuracy:

  1. Given dimensions:

    • Length \( l = 4.5 \) cm
    • Width \( w = 3.5 \) cm
    • Height \( h = 2.5 \) cm
  2. Calculate the products:

    • \( lw = 4.5 \times 3.5 = 15.75 , \text{cm}^2 \)
    • \( lh = 4.5 \times 2.5 = 11.25 , \text{cm}^2 \)
    • \( wh = 3.5 \times 2.5 = 8.75 , \text{cm}^2 \)
  3. Sum the areas of the three pairs of faces: \[ lw + lh + wh = 15.75 + 11.25 + 8.75 = 35.75 , \text{cm}^2 \]

  4. Multiply by 2 to find the total surface area: \[ \text{Surface Area} = 2 \times (lw + lh + wh) = 2 \times 35.75 , \text{cm}^2 = 71.5 , \text{cm}^2 \]

Thus, the surface area of the right rectangular prism is indeed 71.5 cm². Thank you for double-checking, and if you have further questions, feel free to ask!