Respuesta :

aencabo
The answer would be   A = 54raiz (3) + 18raiz (91)
Formula:
 A = Ab + Al Where, Ab=base area A= lateral area

 The area of the base is: Ab = (3/2) * (L ^ 2) * (root (3)) Where, L= side of the hexagon. Substitute: Ab = (3/2) * (6 ^ 2) * (root (3)) Ab = (3/2) * (36) * (root (3)) Ab = 54raiz (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) * (6) * (root ((8) ^ 2 + ((root (3) / 2) * (6)) ^ 2)) Al = 18 * (root (64 + 27)) Al = 18raiz (91)

 The total area is: A = 54raiz (3) + 18raiz (91)

Answer:      

The total area of the given pyramid is  265.24 units²

Step-by-step explanation:

Given : A regular hexagonal pyramid  with height = 8 units and base = 6 units.

We have to find the total area of the given pyramid  

Total surface Area of hexagonal pyramid is given by

[tex]A=\frac{3\sqrt{3}}{2}a^2+3a\sqrt{h^2+\frac{3a^2}{4} }[/tex]

Where a is side length of base

and h is height of pyramid.

We have,

a = 6 units and h = 8 units

Substitute above, we have,

[tex]A=\frac{3\sqrt{3}}{2}(6)^2+3(6)\sqrt{(8)^2+\frac{3(6)^2}{4} }[/tex]

Simplify, we have,

A = 265.24 units²

Thus, The total area of the given pyramid is  265.24 units²