Diagonal of Rectangular Hexagon given Perimeter, Length, Inner Length and Inner Width Calculator

Diagonal of Rectangular Hexagon Formula:

\[ d = \sqrt{(l - l_{Inner})^2 + \left(\frac{P}{2} - l - w_{Inner}\right)^2} \]

Length of Rectangular Hexagon (l):

Inner Length of Rectangular Hexagon (l_Inner):

Perimeter of Rectangular Hexagon (P):

Inner Width of Rectangular Hexagon (w_Inner):

Diagonal of Rectangular Hexagon (d):

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1. What is the Diagonal of Rectangular Hexagon?

The diagonal of a rectangular hexagon is the distance between the inner vertex and the vertex opposite to it of the rectangular hexagon. It represents the longest straight line distance within the hexagon shape.

2. How Does the Calculator Work?

The calculator uses the diagonal formula:

\[ d = \sqrt{(l - l_{Inner})^2 + \left(\frac{P}{2} - l - w_{Inner}\right)^2} \]

Where:

\( d \) — Diagonal of Rectangular Hexagon (m)
\( l \) — Length of Rectangular Hexagon (m)
\( l_{Inner} \) — Inner Length of Rectangular Hexagon (m)
\( P \) — Perimeter of Rectangular Hexagon (m)
\( w_{Inner} \) — Inner Width of Rectangular Hexagon (m)

Explanation: The formula calculates the diagonal by considering the geometric relationships between the outer dimensions, inner dimensions, and perimeter of the rectangular hexagon.

3. Importance of Diagonal Calculation

Details: Calculating the diagonal is important for understanding the spatial dimensions of rectangular hexagons, which is useful in various engineering, architectural, and geometric applications where this shape appears.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure that the inner length is less than the outer length, and that the perimeter value is consistent with the other dimensions for a valid rectangular hexagon.

5. Frequently Asked Questions (FAQ)

Q1: What is a rectangular hexagon?
A: A rectangular hexagon is a six-sided polygon formed by removing two smaller rectangles from the corners of a larger rectangle, creating a shape with both inner and outer dimensions.

Q2: Why is the perimeter divided by 2 in the formula?
A: The division by 2 accounts for the symmetrical nature of the rectangular hexagon and helps relate the perimeter to the individual side lengths in the calculation.

Q3: Can this formula be used for all rectangular hexagons?
A: This specific formula applies to rectangular hexagons where the diagonal is calculated from the inner vertex to the opposite vertex, given the specific parameters of perimeter, length, inner length, and inner width.

Q4: What units should I use for the inputs?
A: The calculator uses meters as the default unit, but any consistent unit of length can be used as long as all inputs are in the same unit.

Q5: What if I get a negative value under the square root?
A: A negative value under the square root would indicate invalid input dimensions that cannot form a proper rectangular hexagon. Please verify your input values.