Answer:
To find the surface area of a regular hexagonal pyramid, we need to find the area of the six triangular faces and the area of the hexagonal base, and then add them together.
The area of each triangular face is given by the formula:
(1/2) x base x height
In this case, the base of each triangle is the side length of the hexagon (8), and the height is the slant height of the pyramid (16). Therefore, the area of each triangular face is:
(1/2) x 8 x 16 = 64
The hexagonal base can be divided into six equilateral triangles, each with side length 8. The area of each equilateral triangle is:
(1/4) x sqrt(3) x side length^2
Plugging in the values, we get:
(1/4) x sqrt(3) x 8^2 = 16sqrt(3)
To find the total surface area, we add the area of the six triangular faces and the area of the hexagonal base:
6 x 64 + 16sqrt(3) = 384 + 16sqrt(3)
Rounding to the nearest tenth, the surface area of the regular hexagonal pyramid is:
398.6 square units (rounded to one decimal place)