calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18, show your work.
To calculate the surface area of a square pyramid, we need to find the sum of the areas of all its faces.
1. The base of the pyramid is a square, so the area of the base is side length squared: A_base = 12^2 = 144 square units.
2. The pyramid has four triangular faces. We need to find the area of one of these triangular faces and then multiply it by 4 to include all four faces.
The area of a triangle can be calculated using the formula A_triangle = (1/2) * base * height.
In a square pyramid, the slant height is the height of each triangular face, and the base length is the base of each triangular face.
Calculating the area of one triangular face:
A_triangle = (1/2) * base * height
A_triangle = (1/2) * 12 * 18
A_triangle = 108 square units
Since there are 4 triangular faces, the total area of the four triangular faces is:
4 * 108 = 432 square units.
3. Finally, to find the surface area, we need to add the area of the base and the area of the four triangular faces:
Surface Area = A_base + A_triangular faces
Surface Area = 144 + 432
Surface Area = 576 square units.
Therefore, the surface area of the square pyramid with a base length of 12 and a slant height of 18 is 576 square units.