CEOMEUR2. A regular octagonal pyramid has a base with side length 13 inches and a slant height of 20 inches. What is the lateral surface area?

To calculate the lateral surface area of a regular octagonal pyramid, you first find the area of one of the triangular faces and then multiply it by the number of faces (which is 8 for an octagonal pyramid). The area \(A\) of each triangular face can be calculated using the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{slant height} \] The base of each triangular face is the side of the octagon, which is 13 inches, and the slant height is 20 inches. So, \[ A = \frac{1}{2} \times 13 \times 20 = 130 \text{ square inches} \] Since there are 8 triangular faces, the total lateral surface area is: \[ \text{Lateral Surface Area} = 8 \times 130 = 1040 \text{ square inches} \] So, the lateral surface area of the pyramid is 1040 square inches.