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 a regular pyramid, we need to calculate the area of the base and the area of the lateral faces.
First, we find the area of the base which is a regular hexagon:
Area of a regular hexagon = 6 * (1/2) * apothem * perimeter of the base
Area of the base = 6 * 0.5 * 6√3 * 12
Area of the base = 216 square meters
Next, we find the area of each lateral face using the formula:
Area of each lateral face = (1/2) * base perimeter * slant height
Area of each lateral face = 0.5 * 12 * 11
Area of each lateral face = 66 square meters
Since there are 6 identical lateral faces, the total area of the lateral faces = 6 * 66 = 396 square meters
Finally, we calculate the total surface area of the pyramid:
Total surface area = area of the base + total area of the lateral faces
Total surface area = 216 + 396
Total surface area = 612 square meters
Therefore, the surface area of the regular pyramid is 612 square meters.