$A B$ is diameter of a circle, $C D$ is a chord equal to the radius of the circle . Find the area of $A B C D$ if radius is $\sqrt{3} c m$

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Solution

Radius of circle $\sqrt{3} c m$
Length of chord is given as $2 \sqrt{r^{2} - d^{2}} = r \sqrt{3 - d^{2}} = \frac{r}{2} 3 - d^{2} = \frac{3}{4} d = \frac{3}{2}$
So the area of $A B C D$ is given as $r \times 2 r \times d \sqrt{3} \times \sqrt{3} \times \frac{3}{2} \frac{9}{2}$

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