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
360 ft.2
360 ft. squared
960 ft.2
960 ft. squared
1,175 ft.2
1,175 ft. squared
480 ft.2
The lateral surface area of the octagonal pyramid can be calculated by finding the area of each of the 8 triangular faces and then adding them together.
Area of one triangular face = (1/2) * base * height
Area of one triangular face = (1/2) * 12 ft * 10 ft
Area of one triangular face = 60 ft²
Total lateral surface area = 8 * 60 ft²
Total lateral surface area = 480 ft²
Therefore, 480 ft² of cedar are needed to cover the lateral surface area of the octagonal pyramid.