Main article: Bramhagupta’s formual
Brahmagupta’s most famous result in geometry is his format for cyclic quadrilaterals. Given the lengths of the sides of any cyclic quadrilateral, Brahmagupta gave an approximate and an exact formula for the figure’s area,
12.21. The approximate area is the product of the halves of the sums of the sides and opposite sides of a triangle and a quadrilateral. The accurate [area] is the square root from the product of the halves of the sums of the sides diminished by [each] side of the quadrilateral.
So given the lengths p, q, r and s of a cyclic quadrilateral, the approximate area
Although Brahmagupta does not explicitly state that these quadrilaterals are cyclic, it is apparent from his rules that this is the case. Heron’s formula is a special case of this formula and it can be derived by setting one of the sides equal to zero.
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