Question

caculate the surface ate of the square pyramid that has a base lenght of 12 and a slant height of 18 show youer work

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the surface area of a square pyramid, you need to add the area of the base to the area of the four triangular faces.

Given:
Base length = 12
Slant height = 18

1. Calculate the area of the base:
Area of a square = side length squared
Area of base = 12 * 12 = 144

2. Calculate the area of each triangular face:
First, calculate the height of each triangular face using the Pythagorean theorem:
height = square root of (slant height^2 - (0.5 * base length)^2)
height = square root of (18^2 - (0.5 * 12)^2)
height = square root of (324 - 36)
height = square root of 288
height ≈ 16.97

Next, calculate the area of each triangular face:
Area of a triangle = 0.5 * base length * height
Area of each triangular face = 0.5 * 12 * 16.97 ≈ 101.82

3. Add the area of the base and the four triangular faces to get the total surface area:
Total surface area = base area + 4 * triangular face area
Total surface area = 144 + 4 * 101.82
Total surface area = 144 + 407.28
Total surface area = 551.28

Therefore, the surface area of the square pyramid is 551.28.