To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces.
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Base Area: The base of the pyramid is a square with side length \( a \). \[ \text{Base Area} = a^2 = (0.5, \text{cm})^2 = 0.25, \text{cm}^2 \]
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Triangular Face Area: The area of one triangular face can be found using the formula for the area of a triangle: \[ \text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} \] Here, the base of each triangle is \( a \) (the side of the square base), and the height of the triangle is \( I \) (the slant height).
Therefore, \[ \text{Area of one triangle} = \frac{1}{2} \times a \times I = \frac{1}{2} \times 0.5, \text{cm} \times 0.8, \text{cm} = \frac{1}{2} \times 0.4, \text{cm}^2 = 0.2, \text{cm}^2 \]
Since there are four triangular faces: \[ \text{Total Area of Triangles} = 4 \times 0.2, \text{cm}^2 = 0.8, \text{cm}^2 \]
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Total Surface Area: The total surface area of the square pyramid is the sum of the base area and the total area of the triangular faces: \[ \text{Total Surface Area} = \text{Base Area} + \text{Total Area of Triangles} = 0.25, \text{cm}^2 + 0.8, \text{cm}^2 = 1.05, \text{cm}^2 \]
Therefore, the surface area of the square pyramid is 1.05 cm².