Sarah is designing a triangular pyramid made of all glass to go on top of a building. All of the faces of the pyramid have a height of 17 feet and a base of 20 feet.
1. First, we need to determine the total surface area of the pyramid.
To do this, we can use the formula:
Surface area = area of base + area of each triangular face
The base of the pyramid is a triangle with a base of 20 feet and a height of 17 feet.
Area of base = 1/2 × base × height = 1/2 × 20 × 17 = 170 square feet
Each of the triangular faces is also a triangle with a base of 20 feet and a height of 17 feet.
Area of each face = 1/2 × base × height = 1/2 × 20 × 17 = 170 square feet
Since there are four faces, we can multiply the area of one face by 4 to get the total area of all four faces.
Total area of all four faces = 4 × 170 = 680 square feet
Therefore, the total surface area of the pyramid is:
Surface area = area of base + area of all four faces
Surface area = 170 + 680 = 850 square feet
2. Next, we need to determine the volume of the pyramid.
To do this, we can use the formula:
Volume = 1/3 × area of base × height
We already know the area of the base (170 square feet) and the height of each face (also 17 feet).
Volume = 1/3 × 170 × 17
Volume = 969.33 cubic feet
Therefore, the volume of the pyramid is approximately 969 cubic feet.