To calculate the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular sides.
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Calculate the area of the base: The base of the square pyramid is a square, and the area of a square is given by the formula:
\[ \text{Area of base} = \text{side}^2 \]
The base length is 12, so:
\[ \text{Area of base} = 12^2 = 144 \]
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Calculate the area of the triangular sides: There are four triangular sides, and each triangle has a base equal to the side of the square (12) and a height equal to the slant height (18). The area of a triangle is given by the formula:
\[ \text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} \]
For one triangle:
\[ \text{Area of triangle} = \frac{1}{2} \times 12 \times 18 = \frac{1}{2} \times 216 = 108 \]
Since there are four triangular sides, the total area of the triangles is:
\[ \text{Total area of triangles} = 4 \times 108 = 432 \]
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Calculate the total surface area: Now, we add the area of the base to the total area of the triangular sides:
\[ \text{Total Surface Area} = \text{Area of base} + \text{Total area of triangles} \] \[ \text{Total Surface Area} = 144 + 432 = 576 \]
So, the surface area of the square pyramid is 576 square units.