Answer
30$cm^{2}$
Work Step by Step
Given, AB = 6 cm, BC =7cm
CD =2 cm, DA = 9 cm
By Brahmaguptas formula, the area of cyclic quadrilateral with sides of length a,b,c and d is
A = $\sqrt (s-a)(s-b)(s-c)(s-d)$
s = $\frac{a+b+c +d}{2}$
AB =a = 6 cm, BC = b = 7 cm
CD = c =2 cm, DA = d = 9 cm
s = $\frac{6+7+2+9}{2}$
=12 cm
A = $\sqrt (12-6)(12 - 7)(12 - 2)(12 - 9)$
=$\sqrt 6*5*10*3$
=30$cm^{2}$
Therefore the area of the cyclic quadrilateral ABCD = 30$cm^{2}$.
