To find the surface area of a square pyramid, you need to calculate the area of its base and the area of its four triangular faces, then add those areas together.
The formula for the surface area (SA) of a square pyramid is:
SA = B + L
Where:
- B is the area of the base.
- L is the total area of the triangular faces.
1. **Calculate the area of the base**: Since the base is a square, if you know the length of one side (let’s say it’s s), the area of the base B is simply:
B = s × s = s²
2. **Calculate the area of the triangular faces**: Each triangular face has a base of length s and a height that we’ll call ht. The area of one triangular face is:
Area of one triangle = (1/2) × base × height = (1/2) × s × ht
Since there are four triangular faces, the total area L will be:
L = 4 × (1/2) × s × ht = 2s × ht
3. **Combine the areas**: Finally, plug the values of B and L into the surface area formula:
SA = s² + 2s × ht
This gives you the total surface area of the square pyramid. Make sure to measure all lengths in the same units, and the final surface area will be in square units.