Long Height of Skewed Three Edged Prism given Volume Calculator

Formula Used:

\[ h_{Long} = \frac{3 \times V}{A_{Base(Even)}} - h_{Short} - h_{Medium} \]

Volume of Skewed Three Edged Prism (V):

m³

Even Base Area of Skewed Three Edged Prism (A_Base(Even)):

m²

Short Height of Skewed Three Edged Prism (h_Short):

Medium Height of Skewed Three Edged Prism (h_Medium):

Long Height of Skewed Three Edged Prism (h_Long):

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1. What is Long Height of Skewed Three Edged Prism?

Long Height of Skewed Three Edged Prism is the length of the longest lateral edge or the maximum vertical distance between top and bottom triangular faces of the Skewed Three Edged Prism.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_{Long} = \frac{3 \times V}{A_{Base(Even)}} - h_{Short} - h_{Medium} \]

Where:

\( h_{Long} \) — Long Height of Skewed Three Edged Prism (m)
\( V \) — Volume of Skewed Three Edged Prism (m³)
\( A_{Base(Even)} \) — Even Base Area of Skewed Three Edged Prism (m²)
\( h_{Short} \) — Short Height of Skewed Three Edged Prism (m)
\( h_{Medium} \) — Medium Height of Skewed Three Edged Prism (m)

Explanation: This formula calculates the longest height of a skewed three-edged prism based on its volume, base area, and the other two heights.

3. Importance of Long Height Calculation

Details: Calculating the long height is essential for understanding the complete geometry of skewed three-edged prisms, which is important in various engineering and architectural applications where non-standard prism shapes are used.

4. Using the Calculator

Tips: Enter volume in cubic meters, base area in square meters, and both short and medium heights in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a Skewed Three Edged Prism?
A: A skewed three-edged prism is a polyhedron with two triangular bases and three rectangular lateral faces that are not perpendicular to the bases.

Q2: Why are there three different heights in this prism?
A: Because the prism is skewed, each of the three lateral edges has a different length, resulting in three distinct heights.

Q3: Can this formula be used for regular prisms?
A: For regular prisms where all heights are equal, this formula would simplify to h = V/A, which is the standard volume formula.

Q4: What are typical applications of skewed three-edged prisms?
A: These prisms are commonly found in architectural designs, structural engineering, and various mechanical components where non-standard geometric shapes are required.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of skewed three-edged prisms, provided accurate input values are given.