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