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
480 ft.2
1,175 ft.2
360 ft.2
To find the lateral surface area of the octagonal pyramid, we first need to calculate the area of each triangular face. Each face is a triangle with a base of 12 feet and a height of 10 feet.
Area of each triangular face = 1/2 * base * height
Area of each triangular face = 1/2 * 12 ft * 10 ft
Area of each triangular face = 60 ft^2
Since there are 8 triangular faces on the octagonal pyramid, the total lateral surface area is:
Total lateral surface area = 8 * 60 ft^2
Total lateral surface area = 480 ft^2
Therefore, you would need 480 square feet of cedar to cover the lateral surface area of the octagonal pyramid. The correct answer is option B: 480 ft^2.