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

Formula Used:

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

Longer Base Edge:

Long Height:

Short Height:

Shorter Top Edge:

Shorter Base Edge:

Longer Top Edge:

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

The Longer Top Edge of a Skewed Three Edged Prism is the length of the longest edge of the triangular face at the top of the prism. It is an important geometric measurement used in various engineering and architectural applications.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

Longer Base Edge — Length of the longest edge of the bottom triangular face (m)
Long Height — Length of the longest lateral edge (m)
Short Height — Length of the shortest lateral edge (m)
Shorter Top Edge — Length of the shortest edge of the top triangular face (m)
Shorter Base Edge — Length of the shortest edge of the bottom triangular face (m)

Explanation: The formula calculates the longer top edge by considering the geometric relationships between the various edges and heights of the skewed three-edged prism.

3. Importance of Calculation

Details: Accurate calculation of the longer top edge is crucial for proper design and construction of skewed three-edged prisms in architectural and engineering applications, ensuring structural integrity and precise measurements.

4. Using the Calculator

Tips: Enter all measurements in meters. Ensure that all values are positive and that the Shorter Top Edge is greater than the Shorter Base Edge to avoid mathematical errors in the square root calculation.

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 rectangular lateral faces that are not perpendicular to the bases.

Q2: When would I need to calculate the Longer Top Edge?
A: This calculation is needed in architectural design, structural engineering, and construction projects involving skewed prismatic structures.

Q3: What units should I use for the inputs?
A: The calculator uses meters as the unit of measurement. Convert other units to meters before inputting values.

Q4: What if I get an error in calculation?
A: Ensure that Shorter Top Edge is greater than Shorter Base Edge, as the square root of a negative number is not defined in real numbers.

Q5: Can this formula be used for other types of prisms?
A: This specific formula is designed for skewed three-edged prisms and may not be applicable to other prism types without modification.