To find the surface area of a pyramid, we need to calculate the area of the base and the area of the three lateral faces.
Given:
Base side length = 9√3 m
Slant height = 18 m
First, calculate the area of the base:
Base area = (side length)^2
Base area = (9√3)^2
Base area = 81 * 3 = 243 m^2
Next, calculate the area of each lateral face:
Lateral face area = (1/2) * (perimeter of base) * slant height
Perimeter of base = 4 * side length = 4 * 9√3 = 36√3 m
Lateral face area = (1/2) * 36√3 * 18
Lateral face area = 324√3 m^2
Since there are three identical lateral faces, the total area of the lateral faces is 3 * 324√3 = 972√3 m^2
Now, add the base area and the total area of the lateral faces to find the total surface area of the pyramid:
Total surface area = base area + lateral face area
Total surface area = 243 + 972√3
Total surface area ≈ 2161.96 m^2
Therefore, the surface area of the pyramid is approximately 2162 m^2.
Find the surface area of the pyramid.
9 StartRoot 3 EndRoot m
18 m
18 m
Question content area bottom
Part 1
The surface area of the pyramid is
enter your response here msquared.
(Do not round until the final answer. Then round to the nearest whole number as needed.)
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