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Let a = 9; b = 12; c = 5; and d = 8.
Using Brahmagupthas formula, area of cyclic quadrilateral is
![\sqrt{(s - a)(s - b)(s - c)(s - d)} \\ s = \frac{a + b + c + d}{2} \\ here \: \: s = \frac{9 + 12 + 5 + 8}{2} = 17 \\ area = \\ \sqrt{(17 - 9)(17 - 12)(17 - 5)(17 - 8)} \\ = \sqrt{8 \times 5 \times 12 \times 9} = 12 \sqrt{30} \sqrt{(s - a)(s - b)(s - c)(s - d)} \\ s = \frac{a + b + c + d}{2} \\ here \: \: s = \frac{9 + 12 + 5 + 8}{2} = 17 \\ area = \\ \sqrt{(17 - 9)(17 - 12)(17 - 5)(17 - 8)} \\ = \sqrt{8 \times 5 \times 12 \times 9} = 12 \sqrt{30}](https://tex.z-dn.net/?f=+%5Csqrt%7B%28s+-+a%29%28s+-+b%29%28s+-+c%29%28s+-+d%29%7D++%5C%5C+s+%3D++%5Cfrac%7Ba+%2B+b+%2B+c+%2B+d%7D%7B2%7D++%5C%5C+here+%5C%3A++%5C%3A+s+%3D++%5Cfrac%7B9+%2B+12+%2B+5+%2B+8%7D%7B2%7D++%3D+17+%5C%5C+area+%3D++%5C%5C++%5Csqrt%7B%2817+-+9%29%2817+-+12%29%2817+-+5%29%2817+-+8%29%7D++%5C%5C++%3D++%5Csqrt%7B8+%5Ctimes+5+%5Ctimes+12+%5Ctimes+9%7D++%3D+12+%5Csqrt%7B30%7D+)
Using Brahmagupthas formula, area of cyclic quadrilateral is
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