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.
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)
1 answer