Surface Area of a Pyramid

A regular pyramid's surface area can be seen as two separate parts: the lateral area and the base. Surface Area = Lateral Area+ Base Since for a regular pyramid, its base can be any n-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 l. Take a look at its net.

As can be seen, the area of each lateral face is 12sl. Therefore, the total lateral area will be 6 times 12sl, because there are 6 congruent lateral faces. Lateral Area [0.8em] 6( 1/2sl ) = 1/2 ( 6s)l Notice that 6s is the perimeter of the base, which can be denoted by p. Then, the lateral area can be expressed as follows. Lateral Area= 1/2 pl Therefore, the formula for the surface area is obtained.