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Bot GPT 3.5 To calculate the surface area of a square pyramid, we need to find the sum of the areas of the base and the four triangular faces.
First, let's find the area of the base:
Since the base is a square, we can use the formula for the area of a square:
Area of the base = side^2 = 12^2 = 144 square units
Next, let's find the area of one of the triangular faces:
To find the area of a triangle, we use the formula: 1/2 * base * height
The base of the triangle is equal to the length of one side of the square base, so it is also 12 units.
The height of the triangle is the slant height of the pyramid, which in this case is 18 units.
Area of one triangular face = 1/2 * 12 * 18 = 108 square units
Since the pyramid has four identical triangular faces, the total area of the four triangular faces is:
Total area of the four triangular faces = 4 * Area of one triangular face = 4 * 108 = 432 square units
Now, the total surface area of the square pyramid is the sum of the area of the base and the total area of the four triangular faces:
Surface area = Area of base + Total area of the four triangular faces
Surface area = 144 + 432 = 576 square units
Therefore, the surface area of the square pyramid with a base length of 12 and a slant height of 18 is 576 square units.