Answer:
Rounding to the nearest hundredth, the surface area of the regular hexagonal pyramid is approximately 663.2 square centimeters.
Step by Step Explanation:
The surface area of a regular hexagonal pyramid can be calculated using the formula:
Surface area = (1/2) x Perimeter of base x Slant height + Base area
To find the perimeter of the hexagonal base, we can use the formula:
Perimeter of hexagon = 6 x Length of one side
Since the base edge length is 8 centimeters, the length of one side of the hexagon is also 8 centimeters. Therefore, the perimeter of the hexagonal base is:
Perimeter of base = 6 x Length of one side = 6 x 8 = 48 centimeters
To find the base area of the pyramid, we can use the formula:
Base area = (3/2) x (Square root of 3) x (Length of one side)^2
Substituting the values, we get:
Base area = (3/2) x (Square root of 3) x (8)^2 = 96(sqrt(3)) square centimeters
Now we can substitute the values into the surface area formula:
Surface area = (1/2) x Perimeter of base x Slant height + Base area
Surface area = (1/2) x 48 x 15 + 96(sqrt(3))
Surface area = 360 + 96(sqrt(3)) square centimeters