Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work. ??? help
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. Area of the base:
Since the base of the square pyramid is a square, we can find the area by squaring the base length:
Base Area = 12^2 = 144 square units
2. Area of the four triangular faces:
Each triangular face is an isosceles triangle with base equal to the side length of the base square (12) and height equal to the slant height of the pyramid (18).
Area of one triangular face = 1/2 * base * height = 1/2 * 12 * 18 = 108 square units
Since there are four triangular faces, the total area of all four faces would be 4 * 108 = 432 square units
3. Total surface area:
Total surface area = Base Area + Area of all faces
Total surface area = 144 + 432 = 576 square units
Therefore, the surface area of the square pyramid is 576 square units.