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Mahavira was an Indian mathematician who extended the mathematics of Brahmagupta. Mahavira is highly respected among Indian mathematicians, because of his establishment of terminology for concepts such as equilateral, and isosceles triangle; rhombus; circle and semi-circle.

The formula given below is known as Brahmagupta’s formula to find the area cyclic quadrilateral with sides of length a, b, c, and d.


Brahmagupta an Indian mathematician discovered this formula in the seventh century. Heron’s formula can be viewed as the special case in which d = 0.

Bhaskara I expressed his idea on how rectangle can be treated as a cyclic quadrilateral. He was the first to open discussion on quadrilaterals with all the four sides unequal and none of the opposite sides parallel.

A polygon that has four sides is called a quadrilateral. The basic elements defining a quadrilateral are its four vertices, its four sides and its four angles. Quadrangle ("four angles") and Tetragon ("four and polygon") are other names for Quadrilateral.


1. If A, B, C and D are four points in a plane such that none of the three are collinear and the line segments AB, BC, CD and DA do not intersect except at their end points, the figure formed by these four lines is called the quadrilateral ABCD.

2. A quadrilateral has four vertices (A, B, C and D), four sides (AB, BC, CD and AD), four angles ( A, B, C and D) AC and BD are the two diagonals.


Convex Quadrilateral and Concave Quadrilateral


A quadrilateral is convex if the line segment joining any two points in the region is completely contained in the region. Otherwise it is concave quadrilateral.
The quadrilateral is convex if and only if the two diagonals intersect at a point that is in the interior. While one diagonal of a concave quadrilateral is inside and the other is outside.

In a convex quadrilateral, the measures of all angles are less than 180°. In a concave quadrilateral, the measure of one of the angles is more than 180°.


In each case the interior is shaded and the two diagonals are shown as dotted lines.


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