Brahmagupta: Mathematical and Astronomical Contributions

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Multiple Choice

Brahmagupta's theorem states that the area of a cyclic quadrilateral is given by: $K = \sqrt{(s-a)(s-b)(s-c)(s-d)}$, where $s$ is the semi-perimeter and $a$, $b$, $c$, and $d$ are the lengths of the sides of the quadrilateral. What is the value of $s$ in terms of the side lengths?

  1. $s = \frac{a + b + c + d}{2}$
  2. $s = \frac{a + b - c - d}{2}$
  3. $s = \frac{a - b + c - d}{2}$
  4. $s = \frac{a - b - c + d}{2}$
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