A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid. T. A. =

The area is given by:
 A = Ab + Al
 Where,
 Ab: base area
 Al: lateral area
 The area of the base is:
 Ab = (3/2) * (L ^ 2) * (root (3))
 Where,
 L: side of the hexagon.
 Substituting we have:
 Ab = (3/2) * (4 ^ 2) * (root (3))
 Ab = (3/2) * (16) * (root (3))
 Ab = 24raiz (3)
 The lateral area is:
 Al = (6) * (1/2) * (b) * (h)
 Where,
 b: base of the triangle
 h: height of the triangle
 Substituting we have:
 Al = (6) * (1/2) * (4) * (6)
 Al = 72
 The total area is:
 A = 24raiz (3) + 72
 Answer:
 A = 24raiz (3) + 72