Cyclic Quadrilateral Area (Brahmagupta Formula)

Enter the four sides a, b, c, d to find the area of a cyclic quadrilateral using Brahmagupta formula. It also returns the perimeter, semiperimeter, and circumradius with a scaled diagram.

Input

Enter the four sides a, b, c, d of a cyclic quadrilateral to compute its area with Brahmagupta formula. The perimeter, semiperimeter, and circumradius are shown too.

Side a

Side b

Side c

Side d

Result

Area

18.973666

Perimeter

Semiperimeter s

Circumradius

3.287286

All sides use the same length unit, so the area is in that unit squared.

How it works

The semiperimeter s is half the sum of the four sides, s = (a + b + c + d) / 2.
The area uses Brahmagupta formula, area = √((s − a)(s − b)(s − c)(s − d)), which holds only for a quadrilateral inscribed in a circle.
The circumradius R is R = √((ab + cd)(ac + bd)(ad + bc)) ÷ (4 × area).
Four sides form such a quadrilateral only when all are positive and the longest side is shorter than the sum of the other three.
All four sides share the same length unit, so the area is in that unit squared.

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