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Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work
To calculate the surface area of a square pyramid, we need to find the sum of the lateral surface area and the base area. The lateral surface area of a square pyramid is given by the formula:
Lateral Surface Area = 0.5 * Perimeter of the base * Slant height
First, let's find the perimeter of the base of the square pyramid:
Perimeter of a square = 4 * side length
Perimeter of the base = 4 * 12 = 48
Now, we can calculate the lateral surface area:
Lateral Surface Area = 0.5 * 48 * 18 = 432
The base area of a square pyramid is given by the formula:
Base Area = side length^2
Base Area = 12^2 = 144
Now, we can add the lateral surface area and the base area to find the total surface area:
Total Surface Area = Lateral Surface Area + Base Area
Total Surface Area = 432 + 144 = 576
Therefore, the surface area of the square pyramid is 576 square units.