Area of Cyclic Quadrilateral given Angle A Calculator

Formula Used:

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

Side A of Cyclic Quadrilateral:

Side D of Cyclic Quadrilateral:

Side B of Cyclic Quadrilateral:

Side C of Cyclic Quadrilateral:

Angle A of Cyclic Quadrilateral:

Area of Cyclic Quadrilateral:

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1. What is the Area of Cyclic Quadrilateral given Angle A?

The area of a cyclic quadrilateral given angle A is calculated using the formula that incorporates the four sides and the angle between two adjacent sides. This formula provides an accurate measurement of the 2-dimensional space occupied by the quadrilateral.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( A \) — Area of Cyclic Quadrilateral (m²)
\( Sa \) — Side A of Cyclic Quadrilateral (m)
\( Sd \) — Side D of Cyclic Quadrilateral (m)
\( Sb \) — Side B of Cyclic Quadrilateral (m)
\( Sc \) — Side C of Cyclic Quadrilateral (m)
\( \angle A \) — Angle A of Cyclic Quadrilateral (radians)

Explanation: The formula calculates the area by taking half of the sum of the products of opposite sides, multiplied by the sine of the included angle.

3. Importance of Area Calculation

Details: Accurate area calculation is crucial for geometric analysis, architectural design, land measurement, and various engineering applications involving cyclic quadrilaterals.

4. Using the Calculator

Tips: Enter all side lengths in meters and the angle in degrees. All values must be positive numbers. The angle should be between 0 and 360 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 use this specific formula?
A: This formula provides an efficient way to calculate the area when you know the four sides and one angle of the cyclic quadrilateral.

Q3: Can this formula be used for any quadrilateral?
A: This formula is specifically designed for cyclic quadrilaterals where all vertices lie on a circle.

Q4: What units should I use for the inputs?
A: Side lengths should be in meters and the angle in degrees. The calculator will automatically convert the angle to radians for the calculation.

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