Skewed Top Area Of Skewed Three Edged Prism Given Longer And Shorter Top Edge Calculator

Formula Used:

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

Skewed Top Perimeter (P_Top(Skewed)):

Longer Top Edge (l_{e(Long Top)}):

Shorter Top Edge (l_{e(Short Top)}):

Skewed Top Area (A_Top(Skewed)):

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

The Skewed Top Area of a Skewed Three Edged Prism refers to the total two-dimensional space enclosed by the triangular face at the top of the prism. This area is calculated using Heron's formula based on the perimeter and edge lengths of the triangular top face.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

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

Explanation: This formula is essentially Heron's formula applied to calculate the area of a triangle when all three sides are known, using the perimeter and two given edges to determine the third edge.

3. Importance of Skewed Top Area Calculation

Details: Calculating the skewed top area is crucial for determining the surface area of the prism, material requirements, structural analysis, and various engineering applications involving three-dimensional geometric shapes.

4. Using the Calculator

Tips: Enter the skewed top perimeter in meters, longer top edge in meters, and shorter top edge in meters. All values must be positive numbers, and the sum of the two edges must be less than the perimeter.

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 use this specific formula?
A: This formula uses Heron's formula to calculate the area of the triangular top face when the perimeter and two edge lengths are known, making it efficient for this specific geometric configuration.

Q3: What are the measurement units?
A: The calculator uses meters for all inputs, but the formula works with any consistent unit of length (cm, mm, inches, etc.).

Q4: What if the input values don't form a valid triangle?
A: The calculator will return an error or invalid result if the sum of any two edges is not greater than the third edge, as required by triangle inequality theorem.

Q5: Can this calculator be used for regular triangles?
A: Yes, this calculator works for any triangular shape, whether regular, isosceles, or scalene, as long as the perimeter and two edge lengths are provided.