The Brahmagupta's formula reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Brahmagupta's formula

Brahmagupta's formula, geometric formula to find the area of any quadrilateral.

Table of contents

1 Basic form 2 Extension to Non-Cyclic Quadrilaterals 3 Related Theorems 4 External Link

Basic form

In its basic and easiest to remember form, Brahmagupta's formula gives the area of a cyclic quadrilateral whose sides have lengths a, b, c, d as:

where s, the semiperimeter, is determined by

Extension to Non-Cyclic Quadrilaterals

In the case of non-cyclic quadrilaterals, Brahmagupta's formula can be extended by considering the measures of two opposite angles of the quadrilateral:

where is half the sum of two opposite angles. (The pair is irrelevant: if the other two angles are taken, half their sum is the supplement of . Since , we have .)

It is a property of cyclic quadrilaterals (and ultimately of inscribed angles) that opposite angles of a quadrilateral sum to . Consequently, in the case of an inscribed quadrilateral, , whence the term , giving the basic form of Brahmagupta's formula.

Related Theorems

Heron's formula for the area of a triangle is the special case obtained by taking d=0.

The relationship between the general and extended form of Brahmagupta's formula is similar to how the Law of Cosines extends the Pythagorean Theorem.

External Link

• MathWorld: Brahmagupta's formula

This is the "Brahmagupta's formula" reference article from the English Wikipedia. All text is available under the terms of the GNU Free Documentation License. See also our Disclaimer.