The surface area of a square pyramid with a base length of 12 and a slant height of 18 is calculated by adding the area of the base (144 square units) to four times the area of each triangular face (108 square units each). The total surface area of the pyramid is found by adding the base area to four times the triangular face area, resulting in a surface area of 576 square units.
To calculate the surface area of a square pyramid, you can use the formula:
Surface Area = Base Area + 4 * (1/2 * base length * slant height)
Given:
Base length = 12 units
Slant height = 18 units
1. Calculate the base area:
Base Area = base length * base length = 12 * 12 = 144 square units
2. Calculate the area of each triangular face:
Triangle Area = 1/2 * base length * slant height = 1/2 * 12 * 18 = 108 square units
3. Calculate the total surface area:
Surface Area = 144 + 4 * 108
Surface Area = 144 + 432
Surface Area = 576 square units
Therefore, the surface area of the square pyramid is 576 square units.