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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Area of the base: Since the base is a square with side length 5 feet, the area of the base is: \[ \text{Area of base} = \text{side} \times \text{side} = 5 , \text{feet} \times 5 , \text{feet} = 25 , \text{square feet}. \]
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Area of the triangular faces: The area of one triangular face is given by the formula: \[ \text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 , \text{feet} \times 10 , \text{feet} = \frac{1}{2} \times 50 , \text{square feet} = 25 , \text{square feet}. \] Since there are 4 triangular faces, the total area of the triangular faces is: \[ \text{Area of triangles} = 4 \times 25 , \text{square feet} = 100 , \text{square feet}. \]
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Total surface area: The total surface area of the pyramid is the area of the base plus the area of the triangular faces: \[ \text{Total surface area} = \text{Area of base} + \text{Area of triangles} = 25 , \text{square feet} + 100 , \text{square feet} = 125 , \text{square feet}. \]
Therefore, the surface area of the pyramid is 125 square feet.