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.
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
1 answer