Calculate the surface area of the square pyramid that has a base of 12 and a slant height of 18
To calculate the surface area of a square pyramid, you need to find the area of the base and the area of the four triangular faces.
1. First, calculate the area of the base:
The base of the square pyramid is a square, so you can use the formula for finding the area of a square:
Area of base = side^2
Area of base = 12^2
Area of base = 144
2. Next, calculate the area of the four triangular faces:
The slant height of the pyramid is 18, and the base of each triangle is 12 (half the length of the square base). To calculate the area of each triangle, you can use the formula:
Area of a triangle = 1/2 * base * height
Area of a triangle = 1/2 * 12 * 18
Area of a triangle = 1/2 * 216
Area of a triangle = 108
Now, you have the area of one triangular face. Since there are four triangular faces on a square pyramid, multiply the area of one triangle by 4 to get the total area of all four:
Total area of triangular faces = 4 * 108
Total area of triangular faces = 432
3. Finally, calculate the total surface area of the square pyramid by adding the area of the base and the area of the four triangular faces:
Total surface area = Area of base + Total area of triangular faces
Total surface area = 144 + 432
Total surface area = 576
Therefore, the surface area of the square pyramid is 576 square units.