Calculate volume and surface area for any right or oblique prism with instant results and step-by-step geometric proofs.
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In geometry, a prism is a three-dimensional solid object with two identical ends (called bases) and flat sides (called lateral faces). The key characteristic of any prism is that it maintains the same cross-section along its entire length.
The general formula for any prism is V = Base Area × Height. However, the specific calculation depends on the base shape.
| Prism Type | Formula | Variables |
|---|---|---|
| Rectangular | V = l × w × h | l=length, w=width, h=prism height |
| Triangular | V = ½(b × h_tri) × L | b=base, h_tri=triangle height, L=length |
| Hexagonal | V = (3√3)/2 × s² × h | s=side length, h=height |
A prism has two identical parallel bases and maintains its thickness throughout. A pyramid has only one base and tapers to a single point (called the apex).
Yes. According to Cavalieri's Principle, the volume of an oblique (slanted) prism is calculated exactly the same way as a right prism: Base Area multiplied by the perpendicular Height.
Our formulas are derived from standard Euclidean geometry and verified against WolframAlpha computational results to ensure accuracy for professional and academic use.
Calculations are for theoretical geometric solids. Real-world material thickness may affect actual internal capacity or external dimensions.