Given
radius of the circle = 6cm
Angle subtended by the inscribed triangle = 120 degres
The formulae below would help ss solve the problem:
[tex]\begin{gathered} Area\text{ of sector = }\frac{\theta}{360}\text{ }\times\pi r^2 \\ Where\text{ r is the radius} \\ \\ Area\text{ of a triangle = }\frac{1}{2}absin\theta \end{gathered}[/tex]
The area of th sahaded part can be found using the formula:
[tex]Area\text{ of shaded part = Area of half circle - Area of the triangle}[/tex]
Substituting the given values:
[tex]\begin{gathered} Area\text{ of shaded part = }\frac{120}{360}\text{ }\times\text{ }\pi\times6^2\text{ - }\frac{1}{2}\text{ }\times\text{ 6}\times6\times sin120 \\ =\text{ 37.6991 - 15.5885} \\ =\text{ 22.1106} \\ \approx\text{ 22.1 cm}^2 \end{gathered}[/tex]
Answer: 22.1 square cm
