Even Base Area Of Skewed Three Edged Prism Given Base Edges Calculator

Formula Used:

\[ A_{Base(Even)} = \sqrt{\frac{l_{long} + l_{medium} + l_{short}}{2} \times \left(\frac{l_{long} + l_{medium} + l_{short}}{2} - l_{long}\right) \times \left(\frac{l_{long} + l_{medium} + l_{short}}{2} - l_{medium}\right) \times \left(\frac{l_{long} + l_{medium} + l_{short}}{2} - l_{short}\right)} \]

Even Base Area:

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

The Even Base Area of a Skewed Three Edged Prism refers to the area of the triangular base of the prism. This calculation uses Heron's formula to determine the area of a triangle when all three side lengths are known.

2. How Does the Calculator Work?

The calculator uses Heron's formula:

\[ A = \sqrt{s(s - a)(s - b)(s - c)} \]

Where:

\( A \) — Area of the triangle
\( s \) — Semi-perimeter = \( \frac{a + b + c}{2} \)
\( a, b, c \) — Three sides of the triangle

Explanation: The formula calculates the area of any triangle when the lengths of all three sides are known, without needing to know the height or angles.

3. Importance of Base Area Calculation

Details: Calculating the base area is fundamental for determining the volume of the prism and understanding its geometric properties. It's essential in various engineering and architectural applications.

4. Using the Calculator

Tips: Enter the lengths of all three 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 rectangular lateral faces that are not perpendicular to the bases.

Q2: Why is it called "even" base area?
A: "Even" refers to the regular triangular base, as opposed to any irregular or skewed faces of the prism.

Q3: What units should I use for the inputs?
A: The calculator expects inputs in meters, but you can use any consistent unit of length as the area will be in square units of that measurement.

Q4: What if the inputs don't form a valid triangle?
A: The calculator requires that the sum of any two sides must be greater than the third side. If this condition isn't met, the inputs don't form a valid triangle.

Q5: Can this formula be used for any triangle?
A: Yes, Heron's formula works for any triangle (acute, right, or obtuse) as long as all three side lengths are known.