Square Pyramid Calculator
Calculate volume, surface area, and all properties of square pyramids
Calculate Square Pyramid Properties
Side length of the square base
Perpendicular height from base to apex
Square Pyramid Results
Example Calculations
Basic Square Pyramid
Given: Base length = 6 cm, Height = 4 cm
Volume: V = (a² × h) / 3 = (6² × 4) / 3 = 48 cm³
Slant Height: s = √(h² + (a/2)²) = √(16 + 9) = 5 cm
Surface Area: A = a² + 2a√((a/2)² + h²) = 36 + 60 = 96 cm²
Egyptian Pyramid Scale
Given: Base length = 230 m, Height = 146 m
Volume: V = (230² × 146) / 3 ≈ 2,583,283 m³
Surface Area: A ≈ 85,714 m² (excluding base)
Square Pyramid Formulas
Volume
V = (a² × h) / 3
Base area × height ÷ 3
Surface Area
A = a² + 2a√((a/2)² + h²)
Base + lateral surface
Slant Height
s = √(h² + (a/2)²)
Face height from base to apex
Lateral Edge
d = √(h² + a²/2)
Corner to apex edge
Pyramid Properties
Has 5 faces (1 square base + 4 triangular faces)
Has 8 edges (4 base + 4 lateral)
Has 5 vertices (4 base corners + 1 apex)
Base diagonal = a√2
All lateral faces are congruent triangles
Real-World Applications
Architecture and building design
Ancient monuments (Egyptian pyramids)
Roof structures and tents
Packaging and container design
Mathematical modeling and education
Understanding Square Pyramids
What is a Square Pyramid?
A square pyramid is a three-dimensional geometric shape with a square base and four triangular faces that meet at a single point called the apex. Each triangular face connects one edge of the square base to the apex, creating a pointed structure.
Key Components
- •Base: Square foundation with side length 'a'
- •Height: Perpendicular distance from base to apex
- •Slant Height: Height of triangular face
- •Lateral Edge: Edge from base corner to apex
Calculation Methods
Volume Formula
V = (a² × h) / 3
One-third of base area times height
Surface Area Formula
A = a² + 2a√((a/2)² + h²)
Base area plus lateral surface area
Slant Height Formula
s = √(h² + (a/2)²)
Using Pythagorean theorem
Remember: All measurements must be in the same units for accurate calculations. The pyramid height is always perpendicular to the base, not along a face.