To find the surface area (SA) of a regular pyramid, we can use formulas that incorporate the base area (BA), the lateral area (LA), the perimeter of the base (p), and the slant height (s). Let's discuss each option provided and determine which ones are correct.
1. Option A: [tex]\( SA = BA - LA \)[/tex]
- This formula subtracts the lateral area from the base area, which does not correctly represent the surface area of a pyramid. The surface area should be the sum of the base area and the lateral area, not the difference.
- This formula is not correct.
2. Option B: [tex]\( SA = BA + LA \)[/tex]
- This formula correctly adds the base area (BA) and the lateral area (LA) to find the surface area. This is a valid formula for the surface area of a regular pyramid.
- This formula is correct.
3. Option C: [tex]\( SA = \frac{1}{2} BA + \frac{1}{2} p s \)[/tex]
- This formula is incorrect because it halves the base area (BA) and adds half the product of the perimeter (p) and the slant height (s). This does not correctly represent the surface area of the pyramid.
- This formula is not correct.
4. Option D: [tex]\( SA = BA \cdot LA \)[/tex]
- This formula multiplies the base area and the lateral area, which is not how the surface area of a pyramid is calculated. Surface area should be the sum of the base area and the lateral area.
- This formula is not correct.
5. Option E: [tex]\( SA = BA + \frac{1}{2} p s \)[/tex]
- This formula correctly adds the base area (BA) and half the product of the perimeter (p) and the slant height (s). This is another valid formula for calculating the lateral area, and thus the surface area of the pyramid.
- This formula is correct.
Based on the analysis of each option, the formulas that can be used to find the surface area of a regular pyramid are:
- B. [tex]\( SA = BA + LA \)[/tex]
- E. [tex]\( SA = BA + \frac{1}{2} p s \)[/tex]
Thus, these two formulas are the valid ones for calculating the surface area of a regular pyramid.
