How to Calculate Square Pyramid
What is Square Pyramid?
A square pyramid calculator computes volume, surface area, slant height, and lateral face area from the base side and pyramid height.
Formula
Volume = (base² × height) / 3; Surface Area = base² + 2 × base × slant height
- b
- Base side length (units)
- h
- Height (units)
- V
- Volume (cubic units)
- l
- Slant height (units)
Step-by-Step Guide
- 1Volume = (1/3) × s² × h
- 2Slant height l = √(h² + (s/2)²)
- 3Lateral surface area = 2 × s × l
- 4Total surface area = s² + 2sl (base + 4 triangular faces)
Worked Examples
Input
Base 6cm, height 4cm
Result
Volume = (1/3)×36×4 = 48 cm³; Slant height = √(16+9) = 5cm; SA = 36+60 = 96 cm²
Frequently Asked Questions
Why is pyramid volume = ⅓ × base × height?
A pyramid is 1/3 the volume of a prism with same base and height. Geometric property.
What's slant height?
Distance from apex along face to base edge midpoint. Different from vertical height.
How many faces does a square pyramid have?
5: one square base + 4 triangular sides.