Long Height of Skewed Three Edged Prism given Surface to Volume Ratio Calculator

Formula Used:

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

Total Surface Area of Skewed Three Edged Prism (TSA):

m²

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

m²

SA:V of Skewed Three Edged Prism (SA:V):

1/m

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):

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The 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:

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

Where:

\( h_{Long} \) — Long Height of Skewed Three Edged Prism (m)
\( TSA \) — Total Surface Area of Skewed Three Edged Prism (m²)
\( A_{Base(Even)} \) — Even Base Area of Skewed Three Edged Prism (m²)
\( SA:V \) — Surface Area to Volume Ratio of Skewed Three Edged Prism (1/m)
\( h_{Short} \) — 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 total surface area, base area, surface-to-volume ratio, and the other two heights.

3. Importance of Long Height Calculation

Details: Calculating the long height is essential for determining the complete geometry of a skewed three-edged prism, which is important in various engineering and architectural applications where precise measurements are required.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, square meters for areas). Ensure all values are positive and the base area and surface-to-volume ratio are greater than zero.

5. Frequently Asked Questions (FAQ)

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

Q2: Why are there three different heights?
A: In a skewed prism, the lateral edges have different lengths, resulting in three distinct heights: short, medium, and long.

Q3: Can this formula be used for regular prisms?
A: For regular prisms where all lateral edges are equal, the formula simplifies as the three heights would be identical.

Q4: What are typical applications of this calculation?
A: This calculation is used in structural engineering, architectural design, and manufacturing where precise geometric measurements of irregular prisms are needed.

Q5: How accurate is this calculation?
A: The accuracy depends on the precision of the input values. The formula provides an exact mathematical relationship between the geometric properties.