Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work. the answer is 576 show the simple way how to solve

Answer 1

To find the surface area of a square pyramid, we need to add the area of the base to the area of each of the four triangular faces.

1. Area of the base:
Since the base is a square, we can find its area by squaring the length of one of its sides.
Area = 12 x 12
Area = 144

2. Area of one of the triangular faces:
To find the area of one of the triangular faces, we need to use the formula for the area of a triangle: 1/2 * base * height.
In this case, the base is 12 (corresponding to one side of the square base) and the height is the slant height, which is 18.
Area = 1/2 * 12 * 18
Area = 1/2 * 216
Area = 108

3. Total surface area:
Now we add the area of the base to the combined area of 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.