what is the surface area of a square pyramid where the base edge is 8ft and the slant height is 16ft
To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces, then add them together.
First, let's find the area of the base, which is a square. The area of a square is found by multiplying the length of one side by itself. In this case, the length of the side is 8ft, so the area of the base is 8ft * 8ft = 64ft².
Next, let's find the area of one of the triangular faces. The formula for the area of a triangle is 1/2 * base * height. In this case, the base is one side of the square, which is 8ft, and the height is the slant height of the pyramid, which is given as 16ft. So the area of one of the triangular faces is 1/2 * 8ft * 16ft = 64ft².
Since there are four triangular faces, the total area of the triangular faces is 4 * 64ft² = 256ft².
Finally, we can find the total surface area of the square pyramid by adding the area of the base and the area of the four triangular faces. The total surface area is 64ft² + 256ft² = 320ft².
Therefore, the surface area of a square pyramid with a base edge of 8ft and a slant height of 16ft is 320 square feet.