Filip is making a crate that is a prism with a square base. The base side length is 8 in. and the height of the prism is 20 in. Which of the following correctly calculates the surface area of this prism?(1 point)

Responses

640 in.2
640 in. squared

656 in.2
656 in. squared

768 in.2
768 in. squared

704 in.2

1 answer

To find the surface area of a square prism, you can use the formula for the surface area of a rectangular prism, adjusted for the square base. The surface area (SA) of a prism can be calculated using the formula:

\[ SA = 2B + Ph \]

Where:

  • \(B\) is the area of the base
  • \(P\) is the perimeter of the base
  • \(h\) is the height of the prism
  1. Calculate the area of the base (B): Since the base is a square with a side length of 8 inches: \[ B = 8^2 = 64 \text{ in}^2 \]

  2. Calculate the perimeter of the base (P): The perimeter of a square is given by: \[ P = 4 \times \text{side length} = 4 \times 8 = 32 \text{ in} \]

  3. Calculate the surface area (SA): Now plug these values into the surface area formula: \[ SA = 2B + Ph \] \[ SA = 2 \times 64 + 32 \times 20 \] \[ SA = 128 + 640 \] \[ SA = 768 \text{ in}^2 \]

Therefore, the correct answer for the surface area of the prism is:

768 in.²