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
1,540 m 2
770 m2
770 m 2
396 m2
396 m 2
749 m2
To find the surface area of the regular hexagonal pyramid, we need to find the area of the base and the area of the six triangular faces.
First, find the area of the base:
The area of a regular hexagon = (3√3/2) * s^2
where s is the length of one side of the base
Plugging in s = 12 meters:
Area of the base = (3√3/2) * 12^2 = (3√3/2) * 144 = 216√3 square meters
Next, find the area of one triangular face:
The area of an isosceles triangle = (1/2) * base * height
Height of the triangle = slant height = 11 meters
Base of the triangle = length of one side of the base = 12 meters
Area of one triangular face = (1/2) * 12 * 11 = 66 square meters
Since there are 6 triangular faces on the pyramid, the total area of the triangular faces = 6 * 66 = 396 square meters
Therefore, the total surface area of the regular hexagonal pyramid = area of the base + total area of the six triangular faces
= 216√3 + 396
≈ 749 square meters
Therefore, the surface area of the regular pyramid shown is 749 m^2. So the closest whole number is 749 m2.