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 area of the base and the area of the four triangular faces.
1. The area of the base:
A = side^2
A = 12^2
A = 144
2. The area of each triangular face:
To find the area of a triangle, we will use the formula:
A = 0.5 * base * height
For a pyramid, the base and height of the triangle are the base length and the slant height respectively.
A = 0.5 * 12 * 18
A = 108
3. Since there are four triangular faces in a square pyramid, we need to calculate the total area of the four triangular faces:
Total area of triangular faces = 4 * 108
Total area of triangular faces = 432
4. Finally, we find the surface area by adding the area of the base and the total area of the triangular faces:
Surface Area = Area of base + Total area of triangular faces
Surface Area = 144 + 432
Surface Area = 576
Therefore, the surface area of the square pyramid is 576 square units.