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)
1,175 ft.
2
480 ft.
2
360 ft.
2
960 ft.
2
The lateral surface area of an octagonal pyramid can be found by adding together the areas of the 8 triangular faces.
First, let's find the area of one triangle:
1/2 * base * height = 1/2 * 12 ft * 10 ft = 60 square feet
Since the gazebo has 8 of these triangles, the total lateral surface area is:
8 * 60 ft^2 = 480 ft^2
Therefore, 480 square feet of cedar are needed to cover the lateral surface area of the octagonal pyramid.