To find the lateral surface area of the octagonal pyramid, we need to calculate the area of the triangular faces that make up the sides of the pyramid.
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Determine the number of triangular faces: Since it's an octagonal pyramid, there are 8 triangular faces.
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Calculate the area of one triangular face: The area \( A \) of a triangle can be computed using the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] In this case, the base of each triangular face is a side of the octagon, which is 12 feet, and the height of each triangular face is 10 feet. \[ A = \frac{1}{2} \times 12 \times 10 = \frac{120}{2} = 60 \text{ square feet} \]
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Calculate the total lateral surface area of the pyramid: Multiply the area of one triangular face by the number of triangular faces: \[ \text{Total lateral surface area} = 8 \times A = 8 \times 60 = 480 \text{ square feet} \]
Thus, the total lateral surface area of the octagonal pyramid is 480 square feet.
Therefore, the answer is: 480 ft.²