Answer: Surface Area= 679.20 ft squared
Volume= 1200 cubic feet.
Explanation:
To find the surface area and volume of a pyramid, we need to know the dimensions of the pyramid. The given dimensions are 15ft, 17ft, 16ft, and 16ft.
To calculate the surface area of a pyramid, we need to find the area of the base and the area of the lateral faces.
1. Base area:
The base of the pyramid is a square, so we can find its area by multiplying the length of one side by itself. Since all sides of the base are equal in a square, the length of one side is 15ft.
Base area = 15ft * 15ft = 225ft^2
2. Lateral face area:
The lateral faces of the pyramid are triangles. To find the area of each triangular face, we need to calculate the base and height of the triangle.
The base of the triangle is the length of one side of the base, which is 15ft.
The height of the triangle can be found using the Pythagorean theorem. The height is the perpendicular distance from the apex (top) of the pyramid to the center of the base. We can use half the length of one side of the base (15ft/2 = 7.5ft) and the slant height (17ft) to find the height.
Using the Pythagorean theorem: height^2 = slant height^2 - half base length^2
height^2 = 17ft^2 - 7.5ft^2
height^2 = 289ft^2 - 56.25ft^2
height^2 = 232.75ft^2
height ≈ 15.24ft (rounded to the nearest hundredth)
Now we can find the area of each triangular face using the base and height:
Lateral face area = (1/2) * base * height
Lateral face area = (1/2) * 15ft * 15.24ft ≈ 113.55ft^2
3. Total surface area:
To find the total surface area, we add the base area and the sum of the lateral face areas:
Total surface area = Base area + Lateral face area
Total surface area = 225ft^2 + 4 * 113.55ft^2 = 225ft^2 + 454.20ft^2 ≈ 679.20ft^2
To calculate the volume of the pyramid, we need the base area and the height of the pyramid.
4. Volume:
The volume of a pyramid can be calculated using the formula:
Volume = (1/3) * base area * height
Volume = (1/3) * 225ft^2 * 16ft = 1200ft^3 (rounded to the nearest tenth)