Question

Consider a regular pyramid where p is the perimeter of the base, s is the slant height, BA is the base area, and LA is the lateral area. What is a valid formula for the surface area? Check all that apply. D A. SA = 2BA+ ' ps D B. SA = BA + 2LA O C. SA = BA + 3pS D D. SA = BA + LA O E. SA = 8• LA

Answer 1

Answer:

The valid formula for the surface area are;

$\begin{gathered} SA=BA+LA \\ SA=BA+\frac{1}{2}ps \end{gathered}$

Explanation:

Given the regular pyramid with;

$\begin{gathered} \text{perimeter of base = p} \\ \text{slant height = s} \\ \text{Base area = BA} \\ \text{Lateral area = LA} \end{gathered}$

The total surface area is the sum of the Base area and the Lateral area.

$SA=BA+LA$

And the formula for calculating the lateral area of the pyramid is;

$\begin{gathered} LA=\frac{1}{2}\times Perimeter\text{ of base }\times slant\text{ height} \\ LA=\frac{1}{2}ps \end{gathered}$

substituting LA into the formula above;

$\begin{gathered} SA=BA+LA \\ SA=BA+\frac{1}{2}ps \end{gathered}$

The valid formula for the surface area are;

$\begin{gathered} SA=BA+LA \\ SA=BA+\frac{1}{2}ps \end{gathered}$