Outer Diagonal of Concave Quadrilateral Calculator

Formula Used:

\[ Outer Diagonal = \sqrt{First Outer Side^2 + Second Outer Side^2 - (2 \times First Outer Side \times Second Outer Side \times \cos(Second Acute Angle))} \]

Outer Diagonal:

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1. What is the Outer Diagonal of Concave Quadrilateral?

The Outer Diagonal of a Concave Quadrilateral is a straight line joining two opposite corners that lies outside the region of the Concave Quadrilateral. It is an important geometric measurement for understanding the properties and relationships between the sides and angles of concave quadrilaterals.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Outer Diagonal = \sqrt{First Outer Side^2 + Second Outer Side^2 - (2 \times First Outer Side \times Second Outer Side \times \cos(Second Acute Angle))} \]

Where:

First Outer Side — First outermost side of the Concave Quadrilateral (m)
Second Outer Side — Second outermost side of the Concave Quadrilateral (m)
Second Acute Angle — Angle formed between second outer and second inner side of the Concave Quadrilateral (°)

Explanation: This formula applies the Law of Cosines to calculate the diagonal length based on the two outer sides and the included angle.

3. Importance of Outer Diagonal Calculation

Details: Calculating the outer diagonal is crucial for geometric analysis, structural design, and understanding spatial relationships in concave quadrilateral shapes. It helps in determining various geometric properties and is essential in engineering and architectural applications.

4. Using the Calculator

Tips: Enter First Outer Side and Second Outer Side in meters, Second Acute Angle in degrees. All values must be positive numbers (sides > 0, angle between 0-90°).

5. Frequently Asked Questions (FAQ)

Q1: What is a concave quadrilateral?
A: A concave quadrilateral is a four-sided polygon with at least one interior angle greater than 180°, causing at least one vertex to point inward.

Q2: How is the outer diagonal different from the inner diagonal?
A: The outer diagonal lies outside the quadrilateral's area, while the inner diagonal lies within the quadrilateral's boundary.

Q3: Can this formula be used for convex quadrilaterals?
A: This specific formula is designed for concave quadrilaterals. Different formulas may apply to convex quadrilaterals.

Q4: What units should be used for the inputs?
A: Sides should be in meters and angles in degrees. The calculator will provide results in meters.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the input values. The result is rounded to 6 decimal places for clarity.