Question

what is the formula for the surface area of a right prism if p = x and h = t?
○ sa = xh
○ sa = \\(\frac{1}{2}xl\\)
○ sa = \\(\frac{1}{3}\pi r^2 t\\)
○ sa = xt + 2b
○ sa = \\(\frac{1}{3}bh\\)

Explanation:

Step1: Recall Prism Surface Area Formula

The formula for the surface area (SA) of a right prism is \( SA = ph + 2B \), where \( p \) is the perimeter of the base, \( h \) is the height of the prism, and \( B \) is the area of the base.

Step2: Substitute Given Values

We are given \( p = x \) and \( h = t \). Substituting these into the formula, we get \( SA = xt + 2B \).

Step3: Eliminate Other Options

• \( SA = xh \) is the lateral surface area (missing the \( 2B \) term for the two bases).
• \( SA=\frac{1}{2}xl \) is for a triangle's area or related, not a prism.
• \( SA = \frac{1}{3}\pi r^{2}t \) is for a cone's volume, not surface area.
• \( SA=\frac{1}{3}Bh \) is for a pyramid's volume, not surface area.

Answer:

D. \( SA = xt + 2B \) (assuming the fourth option is labeled D; if the options are labeled differently, adjust the identifier, but the formula is \( SA = xt + 2B \))