The Brahmagupta’s Formula Calculator is a specialized tool designed to compute the area of a cyclic quadrilateral. A cyclic quadrilateral is a four-sided shape where all its corners lie on a single circle. This calculator simplifies the process by using Brahmagupta’s formula, allowing users to find the area without manual calculations. Whether you are a student, educator, or professional in fields like engineering or architecture, this calculator provides a quick and accurate way to determine the area of cyclic quadrilaterals.

## Formula of Brahmagupta’S Formula Calculator

Area (A) = √((s - a) × (s - b) × (s - c) × (s - d))

Where:

**A**: Area of the cyclic quadrilateral**a, b, c, d**: The lengths of the sides of the quadrilateral**s**: Semiperimeter, calculated as s = (a + b + c + d) ÷ 2

This formula allows users to input the lengths of all four sides of a cyclic quadrilateral to instantly find its area. By calculating the semiperimeter first, the formula ensures that the area is determined accurately based on the given side lengths.

## Quick Reference Table

Term | Description |
---|---|

a, b, c, d | Lengths of the four sides of the quadrilateral |

s | Semiperimeter of the quadrilateral |

A | Area of the cyclic quadrilateral |

π (Pi) | Mathematical constant approximately equal to 3.14159 |

√ | Square root operation |

This table provides a quick overview of the essential terms used in Brahmagupta’s formula. Understanding these terms is crucial for effectively using the calculator and interpreting the results.

## Example of Brahmagupta’S Formula Calculator

Suppose you have a cyclic quadrilateral with the following side lengths:

**a**= 5 units**b**= 6 units**c**= 7 units**d**= 8 units

First, calculate the semiperimeter (s):

s = (5 + 6 + 7 + 8) ÷ 2

s = 26 ÷ 2 = 13 units

Next, apply Brahmagupta’s formula:

A = √((13 - 5) × (13 - 6) × (13 - 7) × (13 - 8))

A = √(1680) ≈ 41 units²

Using the Brahmagupta’s Formula Calculator, you can input these side lengths and instantly obtain the area of approximately 41 square units without performing the manual calculations.

## Most Common FAQs

**1. What is a cyclic quadrilateral?**

A cyclic quadrilateral is a four-sided shape where all four vertices lie on the circumference of a single circle. This property allows the use of Brahmagupta’s formula to calculate its area.

**2. Can Brahmagupta’s Formula be used for any quadrilateral?**

No, Brahmagupta’s Formula specifically applies to cyclic quadrilaterals. For other types of quadrilaterals, different formulas are used to calculate the area.

**3. How accurate is the Brahmagupta’s Formula Calculator?**

The calculator provides highly accurate results as long as the input side lengths form a valid cyclic quadrilateral. It eliminates human error in manual calculations, ensuring precise area measurements.