Question
Solve for the surface area of the square pyramid.
(1 point)
Responses
299.25 ft.2
299.25 ft. squared
819 ft.2
819 ft. squared
522 ft.2
522 ft. squared
148.5 ft.2
(1 point)
Responses
299.25 ft.2
299.25 ft. squared
819 ft.2
819 ft. squared
522 ft.2
522 ft. squared
148.5 ft.2
Answers
Answered by
GPT 3.5
To solve for the surface area of a square pyramid, you need to calculate the area of the base and the area of each triangular face, then add them together.
First, let's calculate the area of the base. Since it is a square, the area is equal to the side squared:
Base area = s^2 = 12^2 = 144 ft^2
Second, let's calculate the area of each triangular face. The formula for the area of a triangle is (1/2)base * height. Since the base of the triangle is the same as the side length of the square base, we can use the height of the pyramid as the height of the triangle.
Using Pythagorean theorem:
h = sqrt(12^2 + 6^2) = sqrt(144 + 36) = sqrt(180) ≈ 13.42 ft
Triangular face area = (1/2) * 12 * 13.42 = 80.52 ft^2
Total triangular face area (since there are 4 triangular faces) = 4 * 80.52 = 322.08 ft^2
Add the base area and the total triangular face area to find the total surface area:
Surface area = Base area + Total triangular face area = 144 + 322.08 = 466.08 ft^2
So, the correct answer is not listed, but the surface area of the square pyramid is 466.08 ft^2.
First, let's calculate the area of the base. Since it is a square, the area is equal to the side squared:
Base area = s^2 = 12^2 = 144 ft^2
Second, let's calculate the area of each triangular face. The formula for the area of a triangle is (1/2)base * height. Since the base of the triangle is the same as the side length of the square base, we can use the height of the pyramid as the height of the triangle.
Using Pythagorean theorem:
h = sqrt(12^2 + 6^2) = sqrt(144 + 36) = sqrt(180) ≈ 13.42 ft
Triangular face area = (1/2) * 12 * 13.42 = 80.52 ft^2
Total triangular face area (since there are 4 triangular faces) = 4 * 80.52 = 322.08 ft^2
Add the base area and the total triangular face area to find the total surface area:
Surface area = Base area + Total triangular face area = 144 + 322.08 = 466.08 ft^2
So, the correct answer is not listed, but the surface area of the square pyramid is 466.08 ft^2.
Answered by
GPT 3.5
No, the surface area of the square pyramid is not any of the options provided. The correct surface area of the square pyramid is 466.08 ft^2.
Answered by
GPT 3.5
I apologize for any confusion earlier. If you have any other questions or need further assistance, please feel free to ask. I'm here to help.