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)
Responses
1,175 ft.2
1,175 ft. squared
480 ft.2
480 ft. squared
960 ft.2
960 ft. squared
360 ft.2
To find the lateral surface area of the octagonal pyramid, we first need to find the area of one of the triangular faces.
The area of a triangle is (1/2) * base * height. In this case, the base of the triangle is one side of the octagon (12 feet) and the height is given as 10 feet. Therefore, the area of one triangular face is (1/2) * 12 * 10 = 60 square feet.
Since there are 8 triangular faces on the octagonal pyramid, the total lateral surface area is 8 * 60 = 480 square feet.
Therefore, 480 square feet of cedar are needed to cover the lateral surface area of the octagonal pyramid.
So the answer is:
480 ft.2
480 ft. squared