Explanation: The angle on the semi-circle is always \(90^\circ\). So, triangle PQR is right triangle. Angle P is \(30^\circ\) so the ratio of the sides will be \(1:\sqrt{3}:2\). \(PR = 12\) cm, so \(PQ = \frac{12}{\sqrt{3}} \times 2 = \frac{24}{\sqrt{3}}\) = diameter. Radius \(r = \frac{12}{\sqrt{3}}\) cm. Area of the circle, \(\pi\times(\frac{12}{\sqrt{3}})^2 = \pi\times\frac{144}{3} = 48\pi\) sq. cm .
