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 use the formula:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
First, let's calculate the base area:
Base Area = side^2
Base Area = 12^2
Base Area = 144
Next, let's calculate the perimeter of the base (since it's a square, all sides are equal):
Perimeter of Base = 4 * side
Perimeter of Base = 4 * 12
Perimeter of Base = 48
Now, let's substitute these values into the formula for surface area:
Surface Area = 144 + (1/2) * 48 * 18
Surface Area = 144 + 24 * 18
Surface Area = 144 + 432
Surface Area = 576
Therefore, the surface area of the square pyramid is 576.