Area of Cyclic Quadrilateral given Perimeter Calculator

Area of Cyclic Quadrilateral Formula:

\[ A = \sqrt{\left(\frac{P}{2}-S_a\right) \times \left(\frac{P}{2}-S_b\right) \times \left(\frac{P}{2}-S_c\right) \times \left(\frac{P}{2}-S_d\right)} \]

Perimeter of Cyclic Quadrilateral:

Side A of Cyclic Quadrilateral:

Side B of Cyclic Quadrilateral:

Side C of Cyclic Quadrilateral:

Side D 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 Brahmagupta's formula, which is a generalization of Heron's formula for quadrilaterals. It provides the area based on the perimeter and the four sides of the cyclic quadrilateral.

2. How Does the Calculator Work?

The calculator uses Brahmagupta's formula:

\[ A = \sqrt{\left(\frac{P}{2}-S_a\right) \times \left(\frac{P}{2}-S_b\right) \times \left(\frac{P}{2}-S_c\right) \times \left(\frac{P}{2}-S_d\right)} \]

Where:

\( A \) — Area of Cyclic Quadrilateral (m²)
\( P \) — Perimeter of Cyclic Quadrilateral (m)
\( S_a \) — Side A of Cyclic Quadrilateral (m)
\( S_b \) — Side B of Cyclic Quadrilateral (m)
\( S_c \) — Side C of Cyclic Quadrilateral (m)
\( S_d \) — Side D of Cyclic Quadrilateral (m)

Explanation: The formula calculates the area by taking the square root of the product of the differences between the semi-perimeter and each side.

3. Importance of Area Calculation

Details: Calculating the area of cyclic quadrilaterals is important in geometry, architecture, and various engineering applications where quadrilateral shapes are used in designs and constructions.

4. Using the Calculator

Tips: Enter the perimeter and all four side lengths in meters. All values must be positive numbers, and the sum of any three sides must be greater than the fourth side for a valid quadrilateral.

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: Does this formula work for all quadrilaterals?
A: No, this formula specifically works for cyclic quadrilaterals where all vertices lie on a circle.

Q3: What are the units of measurement?
A: The calculator uses meters for all inputs, and the result is in square meters (m²).

Q4: What if the calculated area is zero or negative?
A: This indicates that the input values do not form a valid cyclic quadrilateral. The sum of any three sides must be greater than the fourth side.

Q5: Can this formula be used for non-cyclic quadrilaterals?
A: No, for non-cyclic quadrilaterals, other methods like dividing into triangles must be used to calculate the area.