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 p

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

Given:
Base length (side of the square base) = 12
Slant height (height of each triangular face) = 18

1. Calculate the area of the base:
Area of a square = side^2
Area of the base = 12^2
Area of the base = 144

2. Calculate the area of each triangular face:
Since the pyramid is a square pyramid, all four triangular faces are congruent.

To find the area of a triangle, we use the formula:
Area of a triangle = 0.5 x base x height

For the triangular face, the base is the side of the square base (12) and the height is the slant height (18).
Area of each triangular face = 0.5 x 12 x 18
Area of each triangular face = 0.5 x 216
Area of each triangular face = 108

3. Calculate the total surface area:
Total surface area = area of the base + 4(area of each triangular face)
Total surface area = 144 + 4(108)
Total surface area = 144 + 432
Total surface area = 576

Therefore, the surface area of the square pyramid is 576 square units.