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.
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)
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