Question
What is the surface area of a square pyramid where the base edge is 1.5 cm and the slant height is 4 cm? Round your answer to the nearest hundredth.(1 point
Answers
Answered by
GPT 3.5
To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.
1. The area of the base can be calculated as the square of the base edge:
Base area = (1.5 cm)^2 = 2.25 cm^2
2. To find the area of one of the triangular faces, we need to find the height of the pyramid:
Using the Pythagorean theorem: height = sqrt((slant height)^2 - (base edge/2)^2)
height = sqrt(4^2 - (1.5/2)^2)
height = sqrt(16 - 0.5625)
height ≈ sqrt(15.4375)
height ≈ 3.93 cm
Now the area of one triangular face can be calculated as 1/2 base x height:
Face area = 1/2 x 1.5 cm x 3.93 cm ≈ 2.29 cm^2
3. Since there are four triangular faces, the total area of the triangular faces is:
Total triangular faces area = 4 x 2.29 cm^2 = 9.16 cm^2
4. The total surface area is the sum of the areas of the base and the triangular faces:
Total surface area = Base area + Total triangular faces area
Total surface area = 2.25 cm^2 + 9.16 cm^2 = 11.41 cm^2
Therefore, the surface area of the square pyramid is approximately 11.41 cm^2.
1. The area of the base can be calculated as the square of the base edge:
Base area = (1.5 cm)^2 = 2.25 cm^2
2. To find the area of one of the triangular faces, we need to find the height of the pyramid:
Using the Pythagorean theorem: height = sqrt((slant height)^2 - (base edge/2)^2)
height = sqrt(4^2 - (1.5/2)^2)
height = sqrt(16 - 0.5625)
height ≈ sqrt(15.4375)
height ≈ 3.93 cm
Now the area of one triangular face can be calculated as 1/2 base x height:
Face area = 1/2 x 1.5 cm x 3.93 cm ≈ 2.29 cm^2
3. Since there are four triangular faces, the total area of the triangular faces is:
Total triangular faces area = 4 x 2.29 cm^2 = 9.16 cm^2
4. The total surface area is the sum of the areas of the base and the triangular faces:
Total surface area = Base area + Total triangular faces area
Total surface area = 2.25 cm^2 + 9.16 cm^2 = 11.41 cm^2
Therefore, the surface area of the square pyramid is approximately 11.41 cm^2.
Answer
wrong
Answered by
GPT 3.5
I apologize for the mistake in my calculation. Let's correct it.
Given:
Base edge = 1.5 cm
Slant height = 4 cm
To find the surface area of a square pyramid, we need to calculate the area of the base and the four triangular faces.
1. Area of the base:
Area of the base = side length x side length = 1.5 cm x 1.5 cm = 2.25 cm^2
2. Area of each triangular face:
The base edge of the pyramid splits the square base into two right triangles.
The height of each triangle can be found using the Pythagorean theorem:
height = sqrt(slant height^2 - (base edge / 2)^2)
height = sqrt(4^2 - (1.5/2)^2)
height = sqrt(16 - 0.5625)
height = sqrt(15.4375)
height ≈ 3.93 cm
The area of one triangular face is:
Area of one triangular face = (0.5 * base * height) = (0.5 x 1.5 cm x 3.93 cm) = 2.3475 cm^2
3. Total surface area:
Total surface area = Area of base + 4 * Area of one triangular face
Total surface area = 2.25 cm^2 + 4(2.3475 cm^2)
Total surface area = 2.25 cm^2 + 9.39 cm^2
Total surface area = 11.64 cm^2
Therefore, the surface area of the square pyramid (rounded to the nearest hundredth) is 11.64 cm^2.
Given:
Base edge = 1.5 cm
Slant height = 4 cm
To find the surface area of a square pyramid, we need to calculate the area of the base and the four triangular faces.
1. Area of the base:
Area of the base = side length x side length = 1.5 cm x 1.5 cm = 2.25 cm^2
2. Area of each triangular face:
The base edge of the pyramid splits the square base into two right triangles.
The height of each triangle can be found using the Pythagorean theorem:
height = sqrt(slant height^2 - (base edge / 2)^2)
height = sqrt(4^2 - (1.5/2)^2)
height = sqrt(16 - 0.5625)
height = sqrt(15.4375)
height ≈ 3.93 cm
The area of one triangular face is:
Area of one triangular face = (0.5 * base * height) = (0.5 x 1.5 cm x 3.93 cm) = 2.3475 cm^2
3. Total surface area:
Total surface area = Area of base + 4 * Area of one triangular face
Total surface area = 2.25 cm^2 + 4(2.3475 cm^2)
Total surface area = 2.25 cm^2 + 9.39 cm^2
Total surface area = 11.64 cm^2
Therefore, the surface area of the square pyramid (rounded to the nearest hundredth) is 11.64 cm^2.