The roof of a gazebo is in the shape of an octagonal pyramid. Each side of the octagon is 12 feet, the height of each triangular face is 10 feet, and the area of the octagon is 695 square feet. How many square feet of cedar are needed to cover the lateral surface area of the octagonal pyramid?(1 point)
To find the lateral surface area of the octagonal pyramid, we need to calculate the area of each triangular face and then add them all together.
First, we need to find the area of one of the triangular faces. Since the base of the triangle is one side of the octagon (12 feet) and the height is given as 10 feet, we can use the formula for the area of a triangle:
Area of a triangle = 1/2 * base * height
Area of one triangular face = 1/2 * 12 ft * 10 ft = 60 square feet
Since there are eight identical triangular faces on the octagonal pyramid, the total lateral surface area is:
Total lateral surface area = 60 sq ft * 8 = 480 square feet
Therefore, 480 square feet of cedar are needed to cover the lateral surface area of the octagonal pyramid.