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 calculate the area of the base and the area of the four triangular faces.
1. Area of the base:
Since the base of the pyramid is a square, we can use the formula for the area of a square:
Area = side^2
Area = 12^2
Area = 144
2. Area of each triangular face:
To find the area of each triangular face, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
The base of each triangle is the side length of the square base, which is 12. The height is the slant height of the pyramid, which is 18.
Area = (1/2) * 12 * 18
Area = 108
3. Total surface area:
The total surface area of the pyramid is the sum of the base area and the four triangular faces:
Total Surface Area = Base Area + 4(Triangular Face Area)
Total Surface Area = 144 + 4(108)
Total Surface Area = 144 + 432
Total Surface Area = 576
Therefore, the surface area of the square pyramid is 576 square units.