Shorter Top Edge of Skewed Three Edged Prism Given Longer Top and Base Edge Calculator

Formula Used:

\[ \text{Shorter Top Edge} = \sqrt{\text{Shorter Base Edge}^2 + \left(\sqrt{\text{Longer Top Edge}^2 - \text{Longer Base Edge}^2} + \text{Short Height} - \text{Long Height}\right)^2} \]

Shorter Base Edge:

Longer Top Edge:

Longer Base Edge:

Short Height:

Long Height:

Shorter Top Edge:

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1. What is the Shorter Top Edge of Skewed Three Edged Prism?

The Shorter Top Edge of a Skewed Three Edged Prism is the length of the shortest edge of the triangular face at the top of the prism. It is an important geometric parameter that helps define the overall shape and dimensions of the skewed prism.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \text{Shorter Top Edge} = \sqrt{\text{Shorter Base Edge}^2 + \left(\sqrt{\text{Longer Top Edge}^2 - \text{Longer Base Edge}^2} + \text{Short Height} - \text{Long Height}\right)^2} \]

Where:

Shorter Base Edge — Length of the shortest edge of the bottom triangular face (m)
Longer Top Edge — Length of the longest edge of the top triangular face (m)
Longer Base Edge — Length of the longest edge of the bottom triangular face (m)
Short Height — Shortest lateral edge or minimum vertical distance (m)
Long Height — Longest lateral edge or maximum vertical distance (m)

Explanation: This formula calculates the shorter top edge by considering the geometric relationships between the base edges, top edges, and the height differences of the skewed prism.

3. Importance of Shorter Top Edge Calculation

Details: Accurate calculation of the shorter top edge is crucial for determining the complete geometry of skewed three-edged prisms, which is essential in structural engineering, architectural design, and geometric modeling applications.

4. Using the Calculator

Tips: Enter all measurements in meters. Ensure that Longer Top Edge is greater than Longer Base Edge for valid calculation. 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 parallel triangular faces (bases) and three parallelogram lateral faces that are not perpendicular to the bases.

Q2: When is this calculation most useful?
A: This calculation is particularly useful in structural engineering, architectural design, and 3D modeling where precise geometric measurements of skewed prisms are required.

Q3: What are the units of measurement?
A: The calculator uses meters for all measurements, but the formula works with any consistent unit system.

Q4: Are there any limitations to this formula?
A: The formula assumes valid geometric relationships between the edges and heights. If Longer Top Edge is not greater than Longer Base Edge, the square root calculation may result in an invalid value.

Q5: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal inputs with up to 4 decimal places precision for accurate calculations.