The surface area of a square pyramid can be calculated using the formula:
Surface Area = Base Area + Lateral Area
Where:
- Base Area is the area of the square base.
- Lateral Area is the total area of the four triangular faces.
To break it down further:
1. **Calculate the Base Area**: The base of a square pyramid is a square. If the length of one side of the square base is s, then the area of the base is:
Base Area = s²
2. **Calculate the Lateral Area**: The lateral area consists of four triangular faces. To find the area of one triangle, you need the base (which is s) and the height of the triangle (which can be obtained using the slant height of the pyramid). If the slant height is l, then the area of one triangle is:
Triangle Area = (1/2) × base × height = (1/2) × s × l
Thus, the lateral area for all four triangles is:
Lateral Area = 4 × (1/2) × s × l = 2sl
3. **Combine the Areas**: Now, you can add the base area and the lateral area together to get the total surface area of the square pyramid:
Surface Area = s² + 2sl
So, if you know the length of the base and the slant height, you can easily plug those values into the formula to find the surface area of the square pyramid.