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BrahmaGupta formula is for Area of a ''Cyclic Quadrilateral''. It is             Area = √[(s-a)(s-b)(s-c)(s-d)] where a, b, c, d are four sides of a cyclic quadrilateral and s = (a+b+c+d) / 2.

[ Cyclic quadrilateral  is a quadrilateral such that a circle can be drawn passing through all  four of its vertices. OR this may also be defined as a quadrilateral such that all four of its vertices lie on a circle].     
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Brhma Gupta formula is for calculating the area of a cyclic quadrilateral. If all the four vertices of quadrilateral are points on a circle, then it is a cyclic quadrilateral.

Rectangle, square are also cyclic quadrilaterals.

If a, b, c and d are sides of a cyclic quadrilateral then,
semi-perimeter is s = (a + b+ c + d ) / 2

Area = \sqrt{s(s-a)(s-b)(s-c)(s-d)}

This is the generalization of the area of triangle that we are aware of.

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