Area Of Cyclic Quadrilateral Given Angle Between Diagonals Calculator

Formula Used:

\[ \text{Area} = \frac{1}{2} \times ((Sa \times Sc) + (Sb \times Sd)) \times \sin(\angle Diagonals) \]

Side A of Cyclic Quadrilateral:

Side C of Cyclic Quadrilateral:

Side B of Cyclic Quadrilateral:

Side D of Cyclic Quadrilateral:

Angle Between Diagonals:

degrees

Area of Cyclic Quadrilateral:

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1. What is the Area of Cyclic Quadrilateral Formula?

The formula calculates the area of a cyclic quadrilateral (a quadrilateral inscribed in a circle) using the lengths of its four sides and the angle between its diagonals. This formula provides an efficient way to determine the area without needing to know the height or other complex measurements.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Area} = \frac{1}{2} \times ((Sa \times Sc) + (Sb \times Sd)) \times \sin(\angle Diagonals) \]

Where:

\( Sa \) — Side A of the cyclic quadrilateral (meters)
\( Sc \) — Side C of the cyclic quadrilateral (meters)
\( Sb \) — Side B of the cyclic quadrilateral (meters)
\( Sd \) — Side D of the cyclic quadrilateral (meters)
\( \angle Diagonals \) — Angle between the diagonals (degrees)

Explanation: The formula combines the product of opposite sides and uses the sine of the angle between diagonals to compute the area accurately.

3. Importance of Area Calculation

Details: Calculating the area of cyclic quadrilaterals is essential in geometry, architecture, and engineering for designing circular structures and understanding spatial relationships in inscribed polygons.

4. Using the Calculator

Tips: Enter all four side lengths in meters and the angle between diagonals in degrees. All values must be positive numbers with sides > 0 and angle between 0-180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is a cyclic quadrilateral?
A: A cyclic quadrilateral is a four-sided polygon where all vertices lie on a single circle.

Q2: Why is the angle between diagonals important?
A: The angle between diagonals affects the area calculation as it determines the sine component in the formula, which scales the area result.

Q3: Can this formula be used for any quadrilateral?
A: No, this specific formula applies only to cyclic quadrilaterals (those inscribed in a circle).

Q4: What units should I use for the inputs?
A: All side lengths should be in the same units (meters recommended), and the angle should be in degrees.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when correct values are provided, though practical measurements may introduce some error.