Answered

IDNLearn.com provides a collaborative platform for sharing and gaining knowledge. Discover in-depth and trustworthy answers from our extensive network of knowledgeable professionals.

Which formulas can be used to find the surface area of a regular pyramid with a square base where the perimeter of the base is equal to [tex]p[/tex], [tex]s[/tex] is the slant height, [tex]B A[/tex] is the base area, and [tex]L A[/tex] is the lateral area?

Check all that apply.

A. [tex]S A = B A - L A[/tex]

B. [tex]S A = B A + \frac{1}{2} p s[/tex]

C. [tex]S A = \frac{1}{2} B A + \frac{1}{2} p s[/tex]

D. [tex]S A = B A \cdot L A[/tex]

E. [tex]S A = B A + L A[/tex]

Sagot :

GinnyAnsweridn
To find the surface area ([tex]\(SA\)[/tex]) of a regular pyramid with a square base, we need to understand the components that make up the surface area. The surface area of such a pyramid is the sum of its base area ([tex]\(BA\)[/tex]) and its lateral area ([tex]\(LA\)[/tex]).

Here, let’s explore each given formula to determine whether it accurately calculates the surface area:

A. [tex]\( SA = BA - LA \)[/tex]

- This formula subtracts the lateral area from the base area, which isn’t logically correct. The surface area should be the sum of the base area and the lateral area.
- Incorrect

B. [tex]\( SA = BA + \frac{1}{2} p s \)[/tex]

- This formula is correct. The lateral area ([tex]\(LA\)[/tex]) of the pyramid is given by [tex]\( \frac{1}{2} p s \)[/tex] where [tex]\(p\)[/tex] is the perimeter of the base and [tex]\(s\)[/tex] is the slant height.
- Hence, adding the base area ([tex]\(BA\)[/tex]) to the lateral area ([tex]\( \frac{1}{2} p s \)[/tex]) correctly gives us the surface area.
- Correct

C. [tex]\( SA = \frac{1}{2} BA + \frac{1}{2} p s \)[/tex]

- This formula incorrectly calculates half the base area, which does not align with the requirement of the total surface area computation.
- Incorrect

D. [tex]\( SA = BA \cdot LA \)[/tex]

- This formula multiplies the base area by the lateral area, which does not represent the correct computation for the surface area of a pyramid.
- Incorrect

E. [tex]\( SA = BA + LA \)[/tex]

- This formula is correct. It states that the surface area is the sum of the base area ([tex]\(BA\)[/tex]) and the lateral area ([tex]\(LA\)[/tex]), which aligns perfectly with how the surface area of a pyramid is computed.
- Correct

Thus, the two formulas that can be used to find the surface area of a regular pyramid with a square base given the base area ([tex]\(BA\)[/tex]), perimeter of the base ([tex]\(p\)[/tex]), and slant height ([tex]\(s\)[/tex]) are:

- B. [tex]\( SA = BA + \frac{1}{2} p s \)[/tex]
- E. [tex]\( SA = BA + LA \)[/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.