What is the surface area of a square pyramid where the base edge is 8 and the slant height is 16?
To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces.
The area of the base of the pyramid (a square) is equal to the length of one side squared, so in this case it would be 8 squared, which is 64.
To find the area of one triangular face, we can use the formula: 1/2 * base * height.
The base of the triangular face is one side of the base of the pyramid, which is 8.
The height of the triangular face (the slant height of the pyramid) is given as 16.
So, the area of one triangular face would be: 1/2 * 8 * 16 = 64.
Since there are four triangular faces on a square pyramid, the total area of all four faces would be: 4 * 64 = 256.
Finally, to calculate the total surface area of the pyramid, we need to add the area of the base (64) to the area of the four triangular faces (256).
So, the total surface area of the square pyramid is: 64 + 256 = 320 square units.