Answer
$9.26\ cm^2$
Work Step by Step
1. Use the hint, we have $BC=\sqrt {8^2-6^2}=2\sqrt 7$ and the area of the triangle ABC is $K_1=\frac{1}{2}(6)(2\sqrt 7)=6\sqrt 7$
2. The area of the semi-cirlce is $K_2=\frac{1}{2}\pi(\frac{8}{2})^2=8\pi$
3. Thus the shaded area is $K_2-K_1=8\pi-6\sqrt 7\approx9.26\ cm^2$
