Find the surface area of the regular pyramid shown to the nearest whole number. The figure is not drawn to scale.
A regular hexagonal pyramid is shown. The slant height is 11 meters, the length of one side of the base is 12 meters, and the apothem of the base is 6 square root 3 meters.
(1 point)
To find the surface area of the regular hexagonal pyramid, we first need to find the area of the base and then find the lateral area.
1. Area of the base:
Since the base is a regular hexagon, we can calculate the area using the formula for the area of a regular hexagon:
Area = (3√3/2) * s^2, where s is the length of one side of the base.
Area = (3√3/2) * 12^2
Area = (3√3/2) * 144
Area = 216√3 square meters
2. Lateral area:
The lateral area of a regular pyramid can be calculated as:
Lateral area = (Perimeter of base * slant height) / 2
Perimeter of base = 6 * 12 = 72 meters
Lateral area = (72 * 11) / 2
Lateral area = 396 square meters
3. Surface area:
Surface area = Area of base + Lateral area
Surface area = 216√3 + 396
Surface area = 216√3 + 396
Rounded to the nearest whole number, the surface area of the regular hexagonal pyramid is 612 square meters.