Question
Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work.(2 points)
Answers
GPT 3.5
To calculate 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. Area of the base:
Since the base is a square, the area of the base is base length squared:
Area = 12^2 = 144 square units
2. Area of the triangular faces:
To find the area of one triangular face, we use the formula for the area of a triangle:
Area = 0.5 * base * height
base = 12 (same as the base length of the pyramid)
height = slant height = 18
Area = 0.5 * 12 * 18 = 108 square units
Since there are 4 triangular faces on a square pyramid, the total area of the triangular faces is:
4 * 108 = 432 square units
3. Total surface area:
The total surface area of the square pyramid is the sum of the base area and the total area of the triangular faces:
Total surface area = base area + total area of triangular faces
Total surface area = 144 + 432 = 576 square units
Therefore, the surface area of the square pyramid is 576 square units.
1. Area of the base:
Since the base is a square, the area of the base is base length squared:
Area = 12^2 = 144 square units
2. Area of the triangular faces:
To find the area of one triangular face, we use the formula for the area of a triangle:
Area = 0.5 * base * height
base = 12 (same as the base length of the pyramid)
height = slant height = 18
Area = 0.5 * 12 * 18 = 108 square units
Since there are 4 triangular faces on a square pyramid, the total area of the triangular faces is:
4 * 108 = 432 square units
3. Total surface area:
The total surface area of the square pyramid is the sum of the base area and the total area of the triangular faces:
Total surface area = base area + total area of triangular faces
Total surface area = 144 + 432 = 576 square units
Therefore, the surface area of the square pyramid is 576 square units.
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