To calculate the surface area of a pyramid, we can use the formula where p is the perimeter of the base, l is the slant height of the pyramid, and B is the area of the base.
S.A.=1/2pl+B
The base of the pyramid is a regular polygon consisting of six sides that are each 4m long. Let's calculate its perimeter!
p=6s ⇒ p=6( 4)=24m
The area of a regular hexagon equals to the half of the apothem of the hexagon multiplied by its perimeter. We are given that the apothem is 2sqrt(3)m. Let's calculate the area of the base!
B=1/2ap ⇒ B=1/2( 2sqrt(3))(24)=24sqrt(3)m^2
We are also given that the slant height l is 8m. Let's substitute all of these values into the formula for the surface area and calculate it.
