Trapezoidal Prism Volume Calculator

Short Base \( b \):

Long Base \( B \):

Height \( h \):

Length \( \ell \):

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

1. What is a Trapezoidal Prism Volume Calculator?

Definition: This calculator computes the volume of a trapezoidal prism based on the lengths of its short base (\( b \)), long base (\( B \)), height (\( h \)), and length (\( \ell \)).

Purpose: Useful in geometry and engineering for determining the volume of prisms with a trapezoidal base.

2. How Does the Calculator Work?

The calculation is based on the following formula:

\[ V = \frac{(b + B)}{2} \times h \times \ell \]

Unit Conversions:

Input (Length): mm (×0.1), cm (×1), m (×100), in (×2.54), ft (×30.48) to cm
Volume: cm³ (direct), in³ (×0.0610237), ft³ (×0.0000353147), m³ (×0.000001), L (×0.001)

Explanation: All dimensions are converted to cm, the volume is calculated in cm³, and then converted to in³, ft³, m³, and L.

3. Importance of Trapezoidal Prism Volume Calculation

Details: Calculating the volume of a trapezoidal prism is essential in architecture, construction, and design for objects with trapezoidal cross-sections.

4. Using the Calculator

Tips: Enter the short base \( b \), long base \( B \), height \( h \), and length \( \ell \) in mm, cm, m, in, or ft (all must be >0). The result shows the volume in cm³, in³, ft³, m³, and L.

5. Example

Given: Short base \( b = 5 \, \text{m} \), long base \( B = 5 \, \text{m} \), height \( h = 3 \, \text{m} \), length \( \ell = 5 \, \text{m} \).
Calculation: \( V = \frac{(5 + 5)}{2} \times 3 \times 5 = 2.5 \times 3 \times 5 = 37.5 \, \text{m}^3 \).
Converted to cm³: \( 37.5 \, \text{m}^3 = 37500000 \, \text{cm}^3 \).

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