Question

Find the lateral area the regular pyramid. L. A. =

Answer 1

Answer:

$18\sqrt{91}$

Answer 2

Answer: $18\sqrt{91}$

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:

$LA=\frac{p*l}{2}$

Find the apothem of the hexagonal base:

$a=\frac{s}{2tan(\frac{180}{n})}$

Where s is the side length and n is the number of sides the polygon.

$s=6\\n=6$

Then:

 $a=\frac{6}{2tan(\frac{180}{6})}$

$a=3\sqrt{3}$

Apply the Pythagorean  Theorem to find the slant height:

$l=\sqrt{(3\sqrt{3})^2+8^2}=\sqrt{91}$

The perimeter is:

$p=6*s=6*6=36$

Susbtituting values, you obtain:

$LA=\frac{36*\sqrt{91}}{2}=18\sqrt{91}$