Find the lateral area the regular pyramid.

180

Step-by-step explanation:

The general formula for the lateral surface area of a regular pyramid is

L.S.A = 1/2 (p)(l)

where p represents the perimeter of the base and l the slant height

Slant height

The hexagon can be broken down into 6 equilateral triangles.  Each side of the equilateral triangle is equal, therefore, the diagonal is twice the side length of the hexagon and the distance from one vertex to mid is half the diagonal.

By considering a right triangle at the centre, we will apply pythagorus theorem

Hypotenuse² = base² + height²

slantHeight² = 6² + 8²

slantHeight = √(6²+8²)

                   = 10

Perimeter of base

6(6) = 36

L.S.A = 1/2 (36)(10)

         = 180