Volume of a Triangular Prism Calculator

Triangle type:

Base \( b \):

Height \( h \):

Prism Length \( L \):

Side \( a \):

Side \( b \):

Prism Length \( L \):

Side \( a \):

Side \( b \):

Side \( c \):

Prism Length \( L \):

Side \( a \):

Side \( b \):

Angle \( \gamma \) (degrees):

Prism Length \( L \):

Side \( a \):

Angle \( \beta \) (degrees):

Angle \( \gamma \) (degrees):

Prism Length \( L \):

Area of Triangular Face:

Prism Length \( L \):

Volume

Volume (cm³): Volume (m³): Volume (in³): Volume (ft³): Volume (liters):

1. What is a Volume of a Triangular Prism Calculator?

Definition: This calculator computes the volume of a triangular prism based on the dimensions of its triangular base and its length (\( L \)), using various methods to define the base triangle.

Purpose: Useful in geometry, engineering, and architecture for determining the volume of triangular prism-shaped objects (e.g., tents, structural beams).

2. How Does the Calculator Work?

The volume is calculated using the following formulas based on the selected method:

Base and Height: \[ V = \frac{1}{2} \times b \times h \times L \]
Right Triangle: \[ V = L \times \left(\frac{a \times b}{2}\right) \]
3 Sides (SSS): \[ V = \frac{1}{4} \times \sqrt{(a+b+c) \times (-a+b+c) \times (a-b+c) \times (a+b-c)} \times L \]
2 Sides + Angle Between (SAS): \[ V = \frac{1}{2} \times a \times b \times \sin(\gamma) \times L \]
2 Angles + Side Between (ASA): \[ V = \frac{1}{2} \times a \times \left(\frac{a \times \sin(\beta)}{\sin(\beta + \gamma)}\right) \times \sin(\gamma) \times L \]
Area of Triangular Face: \[ V = \text{Triangle Base Area} \times L \]

Unit Conversions:

Input (Length): mm (×0.1), cm (×1), m (×100), in (×2.54), ft (×30.48) to cm
Input (Area): mm² (×0.01), cm² (×1), m² (×10000), in² (×6.4516), ft² (×929.0304) to cm²
Volume (from cm³): m³ (×0.000001), in³ (×0.0610237), ft³ (×0.0000353147), liters (×0.001)

Explanation: All dimensions are converted to cm (and area to cm²), the volume is calculated in cm³, and then converted to m³, in³, ft³, and liters.

3. Importance of Triangular Prism Volume Calculation

Details: Calculating the volume of a triangular prism is essential in architecture (e.g., designing triangular roofs), engineering (e.g., structural analysis), and storage (e.g., determining capacity).

4. Using the Calculator

Tips: Select the method to define the triangular base, then enter the required dimensions and prism length in mm, cm, m, in, or ft (all must be >0, with valid geometric constraints). The result shows the volume in cm³, m³, in³, ft³, and liters.

5. Example

Given (Base and Height): Base \( b = 6 \, \text{cm} \), height \( h = 4 \, \text{cm} \), prism length \( L = 10 \, \text{cm} \).
Volume Calculation: \( V = \frac{1}{2} \times 6 \times 4 \times 10 = 120 \, \text{cm}^3 \).
Conversions:
- \( \text{cm}^3 = 120 \),
- \( \text{m}^3 = 0.00012 \),
- \( \text{in}^3 \approx 7.323 \),
- \( \text{ft}^3 \approx 0.00424 \),
- \( \text{liters} = 0.12 \).

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