To calculate the surface area of a square pyramid, you need to calculate the area of the base and the area of the four triangular faces.
First, calculate the area of the base:
Area of a square = side length x side length
Area of the base = 12 x 12 = 144 square units
Next, calculate the area of each triangular face:
Area of a triangle = 0.5 x base x height
Since the base of each triangular face is the same as the side length of the square base (12) and the slant height is given as 18, we can calculate the height using the Pythagorean theorem:
height = sqrt(18^2 - 12^2) = sqrt(324 - 144) = sqrt(180) ≈ 13.42
Now, calculate the area of each triangular face:
Area of each triangular face = 0.5 x 12 x 13.42 ≈ 80.52 square units
Since there are four triangular faces, the total area of all the triangular faces is:
Total area of all triangular faces = 4 x 80.52 = 322.08 square units
Finally, calculate the total surface area of the square pyramid by adding the area of the base and the area of the four triangular faces:
Surface area = 144 + 322.08 = 466.08 square units
Therefore, the surface area of the square pyramid is 466.08 square units.
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