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)
Responses
1,540 m2
770 m2
396 m2
749 m2
To find the surface area of a regular pyramid, you need to find the sum of the areas of the base and the lateral faces.
First, we calculate the area of the base, which is a regular hexagon:
Area_base = (1/2) * apothem * perimeter_base
Area_base = (1/2) * 6 * √3 * 12 = 36√3 square meters
Next, we find the area of each lateral face:
Area_lateral_face = (1/2) * slant_height * perimeter_base
Area_lateral_face = (1/2) * 11 * 12 = 66 square meters
Since there are 6 identical lateral faces on a regular hexagonal pyramid, we calculate the total lateral area as:
Total_lateral_area = 6 * Area_lateral_face = 6 * 66 = 396 square meters
Lastly, we find the total surface area:
Total_surface_area = Area_base + Total_lateral_area = 36√3 + 396 = 396 + 36√3 ≈ 396 + 36(1.73) = 396 + 62.28 ≈ 458.28 square meters
Rounded to the nearest whole number, the surface area of the regular pyramid is approximately 458 square meters. Therefore, none of the provided responses are correct.