Area of Cyclic Quadrilateral given Angle D Calculator

Formula Used:

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

Side A of Cyclic Quadrilateral:

Side B of Cyclic Quadrilateral:

Side C of Cyclic Quadrilateral:

Side D of Cyclic Quadrilateral:

Angle D of Cyclic Quadrilateral:

rad

Area of Cyclic Quadrilateral:

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

The Area of Cyclic Quadrilateral given Angle D is the amount of 2-dimensional space occupied by the Cyclic Quadrilateral, calculated using the formula that involves the four sides and the angle D of the quadrilateral.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

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

3. Importance of Area Calculation

Details: Accurate area calculation is crucial for various geometric and engineering applications, including land surveying, architectural design, and material estimation.

4. Using the Calculator

Tips: Enter all side lengths in meters and angle D in radians. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is angle D used in this formula?
A: Angle D is one of the angles of the cyclic quadrilateral, and its sine function helps in determining the area based on the given sides.

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

Q4: What are the units of measurement?
A: Sides should be in meters, angle in radians, and the resulting area will be in square meters.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values, assuming the quadrilateral is cyclic.