To determine which formulas can correctly be used to find the surface area (SA) of a right prism, we need to remember the key components involved in calculating the surface area of a right prism.
The surface area [tex]\( SA \)[/tex] of a right prism is given by the sum of:
1. The areas of the two bases ([tex]\( B_A \)[/tex])
2. The lateral area ([tex]\( LA \)[/tex]), which is the perimeter of the base times the height of the prism ([tex]\( p \times h \)[/tex])
The valid formulas for the surface area of the prism must incorporate these components correctly. Let's analyze each option:
A. [tex]\( SA = B_A - \angle A \)[/tex]
- This formula is incorrect because subtracting an angle (given as [tex]\(\angle A\)[/tex]) makes no sense in the context of the surface area calculation for a prism.
B. [tex]\( SA = B_A + \angle A \)[/tex]
- This formula is correct because here [tex]\(\angle A\)[/tex] appears to be a symbol for lateral area (LA). Therefore, this formula simplifies to [tex]\( SA = B_A + LA \)[/tex], which is indeed a standard formula for calculating the surface area of a right prism.
C. [tex]\( SA = \frac{1}{2} B_A + LA \)[/tex]
- This formula is incorrect because halving the base area ([tex]\(B_A\)[/tex]) is not part of the standard surface area formula for a right prism.
D. [tex]\( SA = B_A + p \times h \)[/tex]
- This formula is correct because it correctly identifies the two contributing areas to the surface area: the area of the bases ([tex]\( B_A \)[/tex]) and the lateral area ([tex]\( p \times h \)[/tex]).
E. [tex]\( SA = p + \angle A \)[/tex]
- This formula is incorrect because it incorrectly mixes the perimeter ([tex]\( p \)[/tex]) and an angle (again [tex]\( \angle A \)[/tex] which could be implying [tex]\( LA \)[/tex]), and misses out the area of the bases.
Thus, the valid formulas to find the surface area of a right prism are:
[tex]\[ \text{B: } SA = B_A + LA \][/tex]
[tex]\[ \text{D: } SA = B_A + p \times h \][/tex]
So, the correct answer is:
[tex]\[ [2, 4] \][/tex]
