Answer:
[tex]A_{S} = \frac{p_{b}}{2}\cdot (l_{b}+l)[/tex]
Step-by-step explanation:
The surface area of the regular pyramid is equal to the sum of the base and lateral areas:
[tex]A_{S} = A_{b} + A_{l}[/tex]
Where the base area is equal to:
[tex]A_{b} = \frac{p_{b}\cdot l_{b}}{2}[/tex]
In which [tex]p_{b}[/tex] and [tex]l_{b}[/tex] are the base perimeter and slant, respectively.
And the lateral area is:
[tex]A_{l} = \frac{p_{b}\cdot l}{2}[/tex]
Where [tex]l[/tex] is the side slant.
By substituting and simplifying the expression, the formula of the surface area for a regular pyramid is found:
[tex]A_{S} = \frac{p_{b}\cdot l_{b}}{2}+\frac{p_{b}\cdot l}{2}[/tex]
[tex]A_{S} = \frac{p_{b}}{2}\cdot (l_{b}+l)[/tex]
