Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18.
Show your work. (2 points)
To calculate the surface area of a square pyramid, we need to find the area of the base, the area of the four triangles (each of which has one base equal to the side length of the square base and the other two sides equal to the slant height), and then add them all together.
Given:
Base length = 12
Slant height = 18
1. Area of the base:
Area_base = side^2
Area_base = 12^2
Area_base = 144
2. Area of each triangular face:
Area_triangle = 1/2 * base * height
Area_triangle = 1/2 * 12 * 18
Area_triangle = 1/2 * 216
Area_triangle = 108
Since there are four triangular faces, the total area of all triangular faces is:
Total_area_triangles = 4 * Area_triangle
Total_area_triangles = 4 * 108
Total_area_triangles = 432
3. Total surface area of the square pyramid:
Total_surface_area = Area_base + Total_area_triangles
Total_surface_area = 144 + 432
Total_surface_area = 576
Therefore, the surface area of the square pyramid is 576 square units.