Even Base Area of Skewed Three Edged Prism Given Longer and Medium Base Edge Calculator

Formula Used:

\[ A_{Base(Even)} = \sqrt{\left(\frac{P_{Base(Even)}}{2}\right) \times \left(\frac{P_{Base(Even)}}{2} - l_{e(Long\ Base)}\right) \times \left(\frac{P_{Base(Even)}}{2} - l_{e(Medium\ Base)}\right) \times \left(\frac{P_{Base(Even)}}{2} - (P_{Base(Even)} - l_{e(Long\ Base)} - l_{e(Medium\ Base)})\right)} \]

Even Base Perimeter of Skewed Three Edged Prism (P_Base(Even)):

Longer Base Edge of Skewed Three Edged Prism (l_{e(Long Base)}):

Medium Base Edge of Skewed Three Edged Prism (l_{e(Medium Base)}):

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

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1. What is the Even Base Area of Skewed Three Edged Prism?

The Even Base Area of Skewed Three Edged Prism is the total quantity of two dimensional space enclosed on the triangular face at the bottom of the Skewed Three Edged Prism. It represents the area of the base triangle that forms the foundation of the prism.

2. How Does the Calculator Work?

The calculator uses Heron's formula adapted for the specific case of a skewed three-edged prism:

Where:

\( A_{Base(Even)} \) — Even Base Area (m²)
\( P_{Base(Even)} \) — Even Base Perimeter (m)
\( l_{e(Long\ Base)} \) — Longer Base Edge (m)
\( l_{e(Medium\ Base)} \) — Medium Base Edge (m)
\( l_{e(Short\ Base)} \) — Shorter Base Edge, calculated as \( P_{Base(Even)} - l_{e(Long\ Base)} - l_{e(Medium\ Base)} \)

Explanation: This formula is derived from Heron's formula for calculating the area of a triangle when all three sides are known, using the semi-perimeter concept.

3. Importance of Even Base Area Calculation

Details: Calculating the base area is crucial for determining the volume of the prism, structural analysis, material requirements, and understanding the geometric properties of the skewed three-edged prism.

4. Using the Calculator

Tips: Enter the even base perimeter and the lengths of the longer and medium base edges in meters. All values must be positive numbers that satisfy the triangle inequality theorem.

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 is it called "Even Base"?
A: The term "Even Base" refers to the regular triangular base of the prism, as opposed to any skewed or irregular faces the prism might have.

Q3: What are the constraints for valid input values?
A: The three edges must satisfy the triangle inequality: the sum of any two sides must be greater than the third side, and all values must be positive.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for the given inputs, though practical measurements may introduce some error.

Q5: Can this formula be used for any triangle?
A: Yes, this is essentially Heron's formula and can calculate the area of any triangle when all three side lengths are known.