Geometry
Pyramid Volume Calculator
Volume and surface area of square and rectangular pyramids. Compute pyramid volume using V = ⅓Bh and lateral surface area for any square or rectangular base pyramid.
Live Vector System
Core Dimensions
Analytic Metrics
Surface Area
78.54
Perimeter
31.416
Mathematical Verification
Our engine utilizes double-precision floating-point arithmetic for geometric derivations. For triangles, we implement Heron's Theorem with strict validation to ensure the triangle inequality principle is maintained.
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Solution Methodology
01
Enter Base & Height
Provide base side length a and vertical height h.
02
Compute Slant Height
Calculate l = √(h² + (a/2)²).
03
Compute Volume & SA
Apply V = (1/3)a²h and SA = a² + 2al.
Common Questions
Why is the volume of a pyramid one-third of a prism?
Three congruent pyramids can be assembled to fill one rectangular prism of the same base and height, a fact demonstrable through Cavalieri's principle or integration. This is why the formula is V = (1/3)Bh.
How is slant height different from the pyramid's height?
The vertical height h is measured perpendicularly from the apex straight down to the base center. The slant height l is measured along a triangular face from the apex to the midpoint of a base edge: l = √(h² + (a/2)²) for a square base of side a.