Surface Area of a Square Pyramid Calculator
Calculate total surface area, base area, lateral surface area, and face area of a square pyramid
Calculate Square Pyramid Surface Area
Length of one side of the square base
Perpendicular distance from base to apex
Surface Area Results
Formula used: SA = a² + 2al = 0.00 + 2 × 0 × 0.00
Alternative formula: SA = a² + a√(a² + 4h²) = 0.00 cm²
Components: Base Area + Lateral Surface Area = 0.00 + 0.00 = 0.00 cm²
Example Calculation
Pyramid of Giza Example
Base edge (a): 756 feet
Height (h): 480 feet
Slant height (l): √((756/2)² + 480²) = √(378² + 480²) = 611 feet
Calculation
Base Area = a² = 756² = 571,536 ft²
Lateral Surface Area = 2al = 2 × 756 × 611 = 923,832 ft²
Total Surface Area = 571,536 + 923,832 = 1,495,368 ft²
Square Pyramid Components
Base
Square base with area a²
Triangular Faces
Each with area (al)/2
Total Faces
1 square + 4 triangles
Formula Reference
Total Surface Area
SA = a² + 2al
or SA = a² + a√(a² + 4h²)
Base Area
BA = a²
Lateral Surface Area
LSA = 2al
Slant Height
l = √((a/2)² + h²)
Quick Tips
Base edge is the length of one side of the square base
Height is perpendicular distance from base to apex
Slant height is distance along triangular face to apex
Total surface area includes base + all faces
Understanding Square Pyramid Surface Area
What is Surface Area?
The surface area of a square pyramid is the total area of all its faces. A square pyramid has 5 faces: 1 square base and 4 triangular faces. The surface area is the sum of all these areas.
Components Breakdown
- •Base Area: Area of the square base = a²
- •Face Area: Area of one triangular face = (al)/2
- •Lateral Surface Area: Total area of 4 triangular faces = 2al
- •Total Surface Area: Base + Lateral = a² + 2al
Formula Derivation
SA = Base Area + Lateral Surface Area
SA = a² + 4 × (Face Area)
SA = a² + 4 × (al/2)
SA = a² + 2al
Alternative Formula
When you know the height instead of slant height:
SA = a² + a√(a² + 4h²)
This formula derives from the relationship: l = √((a/2)² + h²)