What is the surface area of a square pyramid where the base edge is 8 ft and slant height is 16 ft
To find the surface area of a square pyramid, you need to find the area of the base and the area of the four triangular faces.
The area of the base is the length of one side of the square, squared. In this case, the base edge is 8 ft, so the area of the base is 8 ft * 8 ft = 64 ft².
The area of each triangular face can be found using the formula A = (1/2) * b * h, where b is the base of the triangle (which is the same as the base edge of the pyramid) and h is the height of the triangle (which is the same as the slant height of the pyramid).
For each triangular face, the base is 8 ft and the slant height is 16 ft, so the area of each triangular face is (1/2) * 8 ft * 16 ft = 64 ft².
There are four triangular faces, so the total area of the triangular faces is 4 * 64 ft² = 256 ft².
Finally, to find the total surface area of the pyramid, you add the area of the base to the area of the triangular faces: 64 ft² + 256 ft² = 320 ft².
Therefore, the surface area of the square pyramid is 320 ft².
To calculate the surface area of a square pyramid, you need to find the areas of the square base and the four triangular faces.
1. Start by calculating the area of the square base:
The base edge of the square pyramid is given as 8 ft.
The formula to find the area of a square is length * width.
Since all sides of a square are equal, the length and the width are both 8 ft.
Area of the base = 8 ft * 8 ft = 64 ft^2.
2. Calculate the area of one triangular face:
The slant height of the pyramid is given as 16 ft.
The slant height is the height of the triangle formed by one of the triangular faces.
To calculate the area of a triangle, you need to know the base and the height.
In this case, the base of the triangular face is the base edge of the square pyramid, which is 8 ft.
The height of the triangle can be found using the Pythagorean theorem: height = √(slant height^2 - (0.5 * base)^2).
Height = √(16 ft^2 - (0.5 * 8 ft)^2)
= √(256 ft^2 - 16 ft^2)
= √(240 ft^2)
= 15.49 ft (rounded to two decimal places).
Now we have the base and height of the triangle, we can calculate its area using the formula: Area = 0.5 * base * height.
Area of one triangular face = 0.5 * 8 ft * 15.49 ft = 61.96 ft^2.
3. Since there are four triangular faces, multiply the area of one triangular face by 4 to get the total area of the four triangular faces:
Total area of the four triangular faces = 61.96 ft^2 * 4 = 247.84 ft^2.
4. Lastly, add the area of the square base to the total area of the four triangular faces to find the surface area of the square pyramid:
Surface area = Area of the base + Total area of the four triangular faces
Surface area = 64 ft^2 + 247.84 ft^2 = 311.84 ft^2.
Therefore, the surface area of the square pyramid with a base edge of 8 ft and a slant height of 16 ft is 311.84 square feet.