To calculate the surface area of a square pyramid, we need to consider both the base area and the area of the triangular faces.
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Base Area: Since the base is a square, the area (A_base) can be calculated as: \[ A_{\text{base}} = \text{side}^2 = 10 , \text{cm} \times 10 , \text{cm} = 100 , \text{cm}^2 \]
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Area of Triangular Faces: A square pyramid has 4 triangular faces. Each triangular face has a base equal to the side length of the square base (10 cm) and a height equal to the slant height (20 cm).
The area of one triangular face (A_triangle) can be calculated as: \[ A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 , \text{cm} \times 20 , \text{cm} = 100 , \text{cm}^2 \]
Therefore, the total area of the 4 triangular faces (A_faces) will be: \[ A_{\text{faces}} = 4 \times A_{\text{triangle}} = 4 \times 100 , \text{cm}^2 = 400 , \text{cm}^2 \]
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Total Surface Area: The total surface area (A_total) of the pyramid is the sum of the base area and the area of the triangular faces: \[ A_{\text{total}} = A_{\text{base}} + A_{\text{faces}} = 100 , \text{cm}^2 + 400 , \text{cm}^2 = 500 , \text{cm}^2 \]
Thus, the surface area of the square pyramid is 500 cm².
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