Question

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)

1,540 m 2

770 m 2

396 m 2

749 m2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of the regular pyramid, we need to calculate the area of the base and the area of the lateral faces separately.

First, let's calculate the area of the base:
The area of a regular hexagon is given by the formula: Area = (3√3/2) * s^2, where s is the length of one side of the base.
Area = (3√3/2) * 12^2
Area = 216√3 m^2 (approximately 374 m^2)

Now, let's calculate the lateral surface area:
The lateral surface area of a regular pyramid is given by the formula: Area = (1/2) * n * s * l, where n is the number of sides of the base, s is the length of one side of the base, and l is the slant height.
Area = (1/2) * 6 * 12 * 11
Area = 396 m^2

Finally, we can calculate the total surface area:
Total surface area = Base area + Lateral surface area
Total surface area = 374 m^2 + 396 m^2
Total surface area = 770 m^2

Therefore, the surface area of the regular pyramid is 770 m^2. The closest whole number answer choice is 770 m^2.