Surface Area of a Pyramid

A regular pyramid's surface area can be seen as two separate parts: the lateral area and the base. Since for a regular pyramid, its base can be any $n\text{-}$sided regular polygon, the lateral area is the sum of the area of $n$ congruent triangles. For example, consider a regular hexagonal pyramid with an edge length $s$ and a slant height $\ell .$ Take a look at its net. As can be seen, the area of each lateral face is $\frac{1}{2}s\ell .$ Therefore, the total lateral area will be $6$ times $\frac{1}{2}s\ell ,$ because there are $6$ congruent lateral faces. Notice that $6s$ is the perimeter of the base, which can be denoted by $p.$ Then, the lateral area can be expressed as follows. Therefore, the formula for the surface area is obtained.