Answer:
Step-by-step explanation:
Given is the hexagonal pyramid.
We know the radius of the base is same as its side.
Find the base area:
- A = 3√3/2a²
- A = 3√3/2*6² = 54√3
Given the height and radius, find the side of the lateral triangular faces:
- [tex]\sqrt{8^2+6^2} =\sqrt{100} =10[/tex]
Each of 6 triangles have sides 10, 10 and 6 units.
Find the area using heron's formula:
- s = P/2 = (10*2 + 6)/2 = 13
- s - a = s - b = 13 - 10 = 3
- s - c = 13 - 6 = 7
- [tex]A = \sqrt{s(s-a)(s-b)(s-c)} =\sqrt{13*3*3*7} =3\sqrt{91}[/tex]
Total surface area:
- [tex]S = 6*3\sqrt{91}+54\sqrt{3} =18\sqrt{91}+54\sqrt{3}[/tex]
Correct choice is B
