Brahmagupta’s Formula Calculator

Brahmagupta’s formula calculates the area of a cyclic quadrilateral (a quadrilateral inscribed in a circle) using the sides of the quadrilateral. This formula is essential in geometry, providing a simple way to find the area without needing additional data like angles or diagonals.

Formula Explanation

For a cyclic quadrilateral with sides \( a \), \( b \), \( c \), and \( d \) and a semi-perimeter \( s \):

\[ s = \frac{a + b + c + d}{2} \]

The area \( A \) is:

\[ A = \sqrt{(s - a)(s - b)(s - c)(s - d)} \]

Example Calculation

For a quadrilateral with sides \( a = 5 \), \( b = 6 \), \( c = 7 \), and \( d = 8 \):

\[ s = \frac{5 + 6 + 7 + 8}{2} = 13 \]

\[ A = \sqrt{(13 - 5)(13 - 6)(13 - 7)(13 - 8)} = \sqrt{8 \times 7 \times 6 \times 5} = \sqrt{1680} \approx 40.99 \]

Application and Usage

This formula is particularly useful in problems involving cyclic quadrilaterals, making it easier to compute areas when all side lengths are known.