formula for rectangular prism: SA =2lw + 2hw + 2lh

use this formula to find the surface area of a rectangular prism that has :
10 m length, 3 m width, and 6 m height

1 answer

To find the surface area (SA) of the rectangular prism using the formula \( SA = 2lw + 2hw + 2lh \), we can plug in the values for length (l), width (w), and height (h).

Given:

  • \( l = 10 , \text{m} \)
  • \( w = 3 , \text{m} \)
  • \( h = 6 , \text{m} \)

Now we can calculate each component of the formula:

  1. \( 2lw = 2 \times 10 \times 3 = 60 , \text{m}^2 \)
  2. \( 2hw = 2 \times 6 \times 3 = 36 , \text{m}^2 \)
  3. \( 2lh = 2 \times 10 \times 6 = 120 , \text{m}^2 \)

Now, sum these values to find the total surface area:

\[ SA = 60 + 36 + 120 = 216 , \text{m}^2 \]

Therefore, the surface area of the rectangular prism is \( 216 , \text{m}^2 \).