Answer: [tex]18\sqrt{91}[/tex]
Step-by-step explanation:
You must apply the following formula for calculate the lateral area the regular pyramid:
Where p is the perimeter of the base and l is the slant height:
[tex]LA=\frac{p*l}{2}[/tex]
Find the apothem of the hexagonal base:
[tex]a=\frac{s}{2tan(\frac{180}{n})}[/tex]
Where s is the side length and n is the number of sides the polygon.
[tex]s=6\\n=6[/tex]
Then:
[tex]a=\frac{6}{2tan(\frac{180}{6})}[/tex]
[tex]a=3\sqrt{3}[/tex]
Apply the Pythagorean Theorem to find the slant height:
[tex]l=\sqrt{(3\sqrt{3})^2+8^2}=\sqrt{91}[/tex]
The perimeter is:
[tex]p=6*s=6*6=36[/tex]
Susbtituting values, you obtain:
[tex]LA=\frac{36*\sqrt{91}}{2}=18\sqrt{91}[/tex]
