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

Formula Used:

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

Skewed Top Perimeter of Skewed Three Edged Prism (P_Top(Skewed)):

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

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

Skewed Top Area of Skewed Three Edged Prism (A_Top(Skewed)):

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1. What is Skewed Top Area of Skewed Three Edged Prism?

The Skewed Top Area of Skewed Three Edged Prism refers to the total quantity of two dimensional space enclosed on the triangular face at the top of the Skewed Three Edged Prism. It is calculated using a modified version of Heron's formula.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( A_{Top(Skewed)} \) — Skewed Top Area (m²)
\( P_{Top(Skewed)} \) — Skewed Top Perimeter (m)
\( l_{e(Long\ Top)} \) — Longer Top Edge (m)
\( l_{e(Medium\ Top)} \) — Medium Top Edge (m)

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

3. Importance of Skewed Top Area Calculation

Details: Calculating the top area is crucial for determining the surface area and volume of the skewed three-edged prism, which has applications in various engineering and architectural contexts.

4. Using the Calculator

Tips: Enter the skewed top perimeter, longer top edge, and medium top edge 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 faces (bases) and three rectangular lateral faces that are not perpendicular to the bases.

Q2: Why is this formula different from standard Heron's formula?
A: This formula expresses the third edge in terms of the perimeter and the other two edges, making it more convenient when the perimeter is known.

Q3: What units should I use for the inputs?
A: The calculator uses meters for all length measurements, but you can use any consistent unit system as long as all inputs are in the same units.

Q4: What if the inputs don't form a valid triangle?
A: The calculator will return an error or invalid result if the inputs violate the triangle inequality theorem (sum of any two sides must be greater than the third side).

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