Superfície Pirâmide (quadrada)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
S_base + S_lateral
About this calculator
The square pyramid surface calculator computes the total surface area of a pyramid with a square base. The total area is the sum of the base area (l²) and the lateral area, which consists of four isosceles triangles. The formula used is S = l² + 2·l·apothem, where l is the side length of the base and apothem is the height of a triangular face (distance from the pyramid's apex to the midpoint of a base edge).
To use the calculator, enter the base side and the apothem of the pyramid. The result is displayed automatically. This tool is useful for geometry students, architects, and professionals who need to calculate materials for covering pyramids or similar structures.
Caution: ensure the apothem is the height of the lateral face, not the pyramid's height. If you have the pyramid's height, you can calculate the apothem using the Pythagorean theorem. Also, the calculator assumes the base is a perfect square; for pyramids with a rectangular base, the formula is different.
Frequently asked questions
What is the difference between apothem and pyramid height?
The apothem is the height of a triangular lateral face, measured from the vertex to the midpoint of a base edge. The pyramid height is the distance from the vertex to the center of the base.
Can I use this calculator for pyramids with a rectangular base?
No, this calculator is specific for square-based pyramids. For a rectangular base, the formula is different and involves two apothem values.
How do I calculate the apothem if I only have the pyramid's height?
Use the Pythagorean theorem: apothem = √(height² + (l/2)²), where l is the base side.
What does 'S' mean in the formula?
S represents the total surface area of the pyramid, including the base and lateral faces.
Does the calculator include the base area?
Yes, the formula S = l² + 2·l·apothem already includes the base area (l²).