Triangular Prism Calculator
Calculate volume, surface area, and geometric properties of triangular prisms with comprehensive analysis. Our calculator supports both base-height method and Heron's formula for any triangle type, providing detailed step-by-step solutions for educational understanding and practical applications in engineering and architecture.
Last updated: December 15, 2024
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Triangle Base & Height
Triangular Prism Results
Primary Calculations:
Triangle Properties:
Detailed Measurements:
Formulas Used:
Calculation Steps:
- Step 1: Calculate triangular prism properties
- Step 2: Prism height = 10 cm
- Step 3: Triangle base = 6 cm, height = 8 cm
- Step 4: Triangle area = ½ × base × height = ½ × 6 × 8 = 24.000 cm²
- Step 5: Hypotenuse = √(6² + 8²) = 10.000 cm
- Step 6: Triangle perimeter = 6 + 8 + 10.000 = 24.000 cm
- Step 8: Volume = Triangle Area × Prism Height = 24.000 × 10 = 240.000 cm³
- Step 9: Lateral surface area = Perimeter × Height = 24.000 × 10 = 240.000 cm²
- Step 10: Total surface area = 2 × Triangle Area + Lateral Area = 2 × 24.000 + 240.000 = 288.000 cm²
Quick Example Result
For triangle base 6 cm, height 8 cm, prism height 10 cm:
Volume = 240.0 cm³
How This Calculator Works
Our triangular prism calculator uses advanced geometric algorithms to compute volume, surface area, and comprehensive properties of triangular prisms. The calculator supports two primary methods: base-height calculation for right triangles and Heron's formula for any triangle type, providing detailed mathematical analysis and step-by-step solutions for educational and professional applications.
Triangular Prism Calculation Methods
Base-Height Method:
Triangle Area = ½ × base × heightHeron's Formula:
Area = √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2Volume & Surface Area:
Volume = Triangle Area × Height, Surface = 2 × Triangle Area + Lateral AreaShows triangular base, height, and 3D prism structure with measurements
Mathematical Foundation
Triangular prisms are fundamental 3D geometric shapes characterized by two parallel triangular bases connected by rectangular lateral faces. The volume calculation extends the 2D triangle area into 3D space by multiplication with height. Heron's formula, dating back to ancient Greece, provides a method to calculate triangle area using only side lengths, making it invaluable when height measurements are unavailable.
- Volume principle: Cross-sectional area multiplied by perpendicular height
- Surface area composition: Two triangular faces plus three rectangular lateral faces
- Triangle classification: Equilateral, isosceles, scalene, and right triangle properties
- Heron's formula: Universal triangle area calculation using semi-perimeter method
Sources & References
- Geometry Textbook Series - 3D Shapes and Volume CalculationsComprehensive coverage of prism geometry and calculation methods
- Khan Academy - Geometry: Volume and Surface AreaInteractive lessons on 3D shape calculations and Heron's formula
- Wolfram MathWorld - Triangular Prism and Heron's FormulaMathematical definitions and properties of triangular prisms
Need help with other 3D shapes? Check out our cylinder calculator and rectangular prism calculator.
Get Custom Calculator for Your BusinessExample Calculation
Given Measurements:
- Triangle Base: 6 cm
- Triangle Height: 8 cm
- Prism Height: 10 cm
- Method: Base-Height
Calculation Steps:
- Triangle area = ½ × 6 × 8 = 24 cm²
- Hypotenuse = √(6² + 8²) = 10 cm
- Perimeter = 6 + 8 + 10 = 24 cm
- Volume = 24 × 10 = 240 cm³
- Surface area = 2 × 24 + 24 × 10 = 288 cm²
Result: Volume = 240.0 cm³, Surface Area = 288.0 cm²
This right triangular prism has a triangle area of 24.0 cm² and forms a right triangle base.
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