Volume of a Triangular Prism Calculator
Calculate triangular prism volume using 6 different methods with step-by-step solutions
Calculate Triangular Prism Volume
Volume Results
Step-by-Step Solution
1. Calculate triangle area: A = ½ × base × height
2. A = ½ × 0 × 0 = 0.0000 cm²
3. Calculate volume: V = base area × length
4. V = 0.0000 × 0 = 0.0000 cm³
Example Calculation
Right Triangle Prism Example
Triangle: Right triangle with sides 3 cm and 4 cm
Prism length: 10 cm
Triangle area: ½ × 3 × 4 = 6 cm²
Volume: 6 × 10 = 60 cm³
Three Sides Example
Triangle sides: 3, 4, 5 cm
Semi-perimeter: s = (3+4+5)/2 = 6 cm
Area (Heron's): √[6×3×2×1] = √36 = 6 cm²
Volume: 6 × 8 = 48 cm³ (length = 8 cm)
Key Formulas
Basic Volume
V = Base Area × Length
Triangle Area (Base × Height)
A = ½ × base × height
Right Triangle Area
A = ½ × a × b
Heron's Formula
A = √[s(s-a)(s-b)(s-c)]
where s = (a+b+c)/2
Two Sides + Angle
A = ½ × a × b × sin(γ)
Triangular Prism Properties
Faces: 5 (2 triangular, 3 rectangular)
Edges: 9
Vertices: 6
Base: Two parallel triangular faces
Cross-section: Same triangular shape throughout
Quick Tips
Choose the method based on available measurements
Right triangle method is fastest for 90° triangles
Heron's formula works for any triangle
Triangle inequality: a + b > c for all sides
Sum of angles in triangle = 180°
Understanding Triangular Prism Volume
What is a Triangular Prism?
A triangular prism is a three-dimensional shape with two parallel triangular bases connected by rectangular faces. The volume represents the amount of space enclosed within this prism.
Volume Formula
The volume of any prism equals the area of its base times its height (or length). For triangular prisms:
Volume = Triangle Area × Prism Length
Common Applications
- •Architecture and construction
- •Engineering design
- •Material volume calculations
- •Packaging and containers
Calculation Methods
Base and Height
Most direct method when you know the triangle's base and perpendicular height.
Right Triangle
Simplified calculation for right-angled triangles using the two perpendicular sides.
Three Sides (Heron's)
Universal method that works for any triangle when all three sides are known.
Two Sides + Angle
Uses trigonometry when you know two sides and the included angle.
Two Angles + Side
Advanced method using the law of sines for complex triangle measurements.
Pre-calculated Area
Direct method when the triangular base area is already known.