Answer:
[tex]36\pi -18\sqrt{7}[/tex]
Step-by-step explanation:
Every inscribed right triangle has its hypotenuse as the same size of the Diameter. Assuming that, this is the case check the picture below.
So the hypotenuse= D=2R=12
- Shaded Area = Area of the Circle- Area of the Triangle
[tex]A_{circle}=\pi (6)^{2}=36\pi[/tex]
Finding the Triangle base via the Pythagorean Theorem
[tex]a^2=b^2+c^2\\12^2=9^2+c^2\\144-81=c^2\\c=\sqrt{63}\\c=3\sqrt{7}\approx 7.94[/tex]
Now plugging in the base of the triangle on that formula:
[tex]A=\frac{bh}{2}\\A=\frac{3\sqrt{7}*12}{2}\\A=18\sqrt{7}[/tex]
Finally,
Shaded Area = [tex]36\pi -18\sqrt{7} cm^{2} \approx 65.48 cm^{2}[/tex]
