Area Of Cyclic Quadrilateral Given Angle C Calculator

Area Of Cyclic Quadrilateral Formula:

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

Side A of Cyclic Quadrilateral:

Side D of Cyclic Quadrilateral:

Side B of Cyclic Quadrilateral:

Side C of Cyclic Quadrilateral:

Angle C of Cyclic Quadrilateral:

Area of Cyclic Quadrilateral:

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1. What is the Area of Cyclic Quadrilateral Formula?

The area of a cyclic quadrilateral can be calculated using the formula that involves the product of opposite sides and the sine of the included angle. This formula provides an accurate measurement of the 2-dimensional space occupied by the cyclic quadrilateral.

2. How Does the Calculator Work?

The calculator uses the area formula:

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

Where:

\( Sa \) — 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)
\( \angle C \) — Angle C of Cyclic Quadrilateral (radians)

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

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 four side lengths in meters and angle C 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 use this specific formula?
A: This formula provides an efficient way to calculate the area when you know the lengths of all four sides and one angle.

Q3: What units should I use for the inputs?
A: Side lengths should be in meters and angle in degrees. The calculator will convert the angle to radians internally.

Q4: Are there limitations to this formula?
A: This formula works specifically for cyclic quadrilaterals and requires knowledge of all four sides and one angle.

Q5: Can I use this for non-cyclic quadrilaterals?
A: No, this formula is specifically designed for cyclic quadrilaterals where all vertices lie on a circle.