Area Of Rectangular Hexagon Given Diagonal, Length, Short Length And Width Calculator

Formula Used:

\[ A = (l \times w) - ((l - l_{Short}) \times (w - \sqrt{d^2 - l_{Short}^2})) \]

Length of Rectangular Hexagon:

Width of Rectangular Hexagon:

Short Length of Rectangular Hexagon:

Diagonal of Rectangular Hexagon:

Area of Rectangular Hexagon:

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1. What is the Area of Rectangular Hexagon?

The Area of Rectangular Hexagon is the amount of 2-dimensional space covered or occupied by the figure. It is calculated by subtracting the area of the cut rectangular portion from the original rectangle's area.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = (l \times w) - ((l - l_{Short}) \times (w - \sqrt{d^2 - l_{Short}^2})) \]

Where:

\( A \) — Area of Rectangular Hexagon (m²)
\( l \) — Length of Rectangular Hexagon (m)
\( w \) — Width of Rectangular Hexagon (m)
\( l_{Short} \) — Short Length of Rectangular Hexagon (m)
\( d \) — Diagonal of Rectangular Hexagon (m)

Explanation: The formula calculates the area by first finding the area of the original rectangle and then subtracting the area of the cut rectangular portion.

3. Importance of Area Calculation

Details: Calculating the area of a rectangular hexagon is important in various fields including architecture, engineering, and design where this specific shape might be used in structures or components.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure that the diagonal is greater than the short length to maintain mathematical validity. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rectangular Hexagon?
A: A Rectangular Hexagon is a six-sided polygon formed by cutting a smaller rectangle from a larger rectangle, resulting in a shape with six sides.

Q2: Why is the square root function used in the formula?
A: The square root function is used to calculate the remaining width after the cut, based on the Pythagorean theorem applied to the diagonal and short length.

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

Q4: What if the diagonal is smaller than the short length?
A: The calculation would result in a negative value under the square root, which is mathematically invalid. The diagonal must always be greater than the short length.

Q5: Can this calculator be used for other polygon shapes?
A: No, this calculator is specifically designed for rectangular hexagons with the given parameters of length, width, short length, and diagonal.