1. What is the Area of Cyclic Quadrilateral Formula?

The formula for calculating the area of a cyclic quadrilateral (Brahmagupta's formula) is based on the semiperimeter and the four sides of the quadrilateral. It provides an accurate area calculation for any quadrilateral that can be inscribed in a circle.

2. How Does the Calculator Work?

The calculator uses Brahmagupta's formula:

Where:

• \( A \) — Area of the cyclic quadrilateral
• \( s \) — Semiperimeter of the quadrilateral
• \( Sa \) — Length of side A
• \( Sb \) — Length of side B
• \( Sc \) — Length of side C
• \( Sd \) — Length of side D

Explanation: This formula calculates the area of any cyclic quadrilateral using only the lengths of its four sides and the semiperimeter.

3. Importance of Area Calculation

Details: Accurate area calculation is crucial for geometry applications, construction planning, land surveying, and various engineering fields where cyclic quadrilaterals are encountered.

4. Using the Calculator

Tips: Enter the semiperimeter and all four side lengths in meters. All values must be positive numbers. The semiperimeter should be greater than each individual side length.

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 is this formula called Brahmagupta's formula?
A: It's named after the Indian mathematician Brahmagupta who discovered this formula in the 7th century.

Q3: Can this formula be used for all quadrilaterals?
A: No, this formula only works for cyclic quadrilaterals (those that can be inscribed in a circle).

Q4: What units should I use for the inputs?
A: The calculator uses meters, but you can use any consistent unit of length as long as all measurements are in the same unit.

Q5: What if I get a negative value under the square root?
A: A negative value indicates that the given sides cannot form a cyclic quadrilateral. Check your measurements.