To find the lateral surface area of the octagonal pyramid, we need to calculate the area of the triangular faces first.
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Determine the number of triangular faces: Since the base of the pyramid is an octagon, there will be 8 triangular faces.
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Calculate the area of one triangular face: The area of a triangular face can be calculated using the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] The base of each triangular face is equal to one side of the octagon (12 feet) and the height is given as 10 feet.
\[ \text{Area of one triangular face} = \frac{1}{2} \times 12 \times 10 = 60 \text{ ft}^2 \]
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Calculate the total area of all triangular faces: Since there are 8 triangular faces, the total lateral surface area (LSA) is: \[ \text{Total LSA} = 8 \times \text{Area of one triangular face} = 8 \times 60 = 480 \text{ ft}^2 \]
Thus, the total lateral surface area of the octagonal pyramid is 480 square feet.
The correct answer is: 480 ft.²