Question

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.

Answer 1

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

Answer 2

The answer would be  A = 24raiz (3) + 72
Formula:
 A = Ab + Al Where, Ab= base area Al= lateral area

The base are:
 Ab = (3/2) * (L ^ 2) * (root (3)) Where, L= side of the hexagon.

 Substitute:
 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
 Substitute: Al = (6) * (1/2) * (4) * (6) Al = 72 The total area is: A = 24raiz (3) + 72