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
1,175 ft.2
1,175 ft. squared
480 ft.2
480 ft. squared
360 ft.2
The lateral surface area of the octagonal pyramid can be calculated by finding the sum of the areas of the 8 triangular faces.
The area of each triangular face can be calculated using the formula: (1/2)base x height.
The base of each triangle is the side of the octagon, which is 12 feet. The height of each triangular face is given as 10 feet.
Area of each triangular face = (1/2) x 12 x 10 = 60 square feet.
Area of all 8 triangular faces = 8 x 60 = 480 square feet.
Therefore, 480 square feet of cedar are needed to cover the lateral surface area of the octagonal pyramid.
The answer is:
480 ft.2
480 ft. squared