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
960 ft.2
960 ft. squared
360 ft.2
360 ft. squared
480 ft.2
480 ft. squared
1,175 ft.2
To find the lateral surface area of the octagonal pyramid, we first need to find the area of one triangular face and then multiply it by the number of faces.
The area of one triangular face can be found using the formula: (1/2) * base * height
= (1/2) * 12 ft * 10 ft
= 60 ft^2
Since there are 8 triangular faces, the total lateral surface area of the pyramid is:
60 ft^2 * 8 = 480 ft^2
Therefore, 480 square feet of cedar are needed to cover the lateral surface area of the octagonal pyramid.
So the correct answer is:
480 ft. squared.