1. What is Brahmagupta's Formula?

Brahmagupta's formula calculates the area of a cyclic quadrilateral (a quadrilateral whose vertices all lie on a single circle) given the lengths of its four sides. It is a generalization of Heron's formula for triangles.

2. How Does the Calculator Work?

The calculator uses Brahmagupta's formula:

Where:

• \( s = \frac{a + b + c + d}{2} \) — Semiperimeter
• \( a, b, c, d \) — Lengths of the four sides

Explanation: The formula calculates the area of any cyclic quadrilateral using only the side lengths, without requiring angle measurements.

3. Importance of Cyclic Quadrilateral Area Calculation

Details: Accurate area calculation is crucial for geometry problems, architectural design, land surveying, and various engineering applications involving quadrilateral shapes that can be inscribed in a circle.

4. Using the Calculator

Tips: Enter all four side lengths in meters. All values must be positive numbers. The quadrilateral must be cyclic (able to be inscribed in a circle) for the formula to be 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. Opposite angles sum to 180 degrees.

Q2: Does this formula work for all quadrilaterals?
A: No, it only works for cyclic quadrilaterals. For general quadrilaterals, more complex formulas involving angles are needed.

Q3: What are some real-world applications?
A: Architecture (designing circular structures), land surveying (calculating irregular plot areas), and mechanical engineering (designing circular components).

Q4: What if my quadrilateral isn't cyclic?
A: The formula will not give the correct area. You would need to use Bretschneider's formula or divide the quadrilateral into triangles.

Q5: Can this formula be used for triangles?
A: Yes, by setting one side to zero, it reduces to Heron's formula for triangles.