We will determine the area of the green section as follows:
[tex]A=r^2\cdot\frac{\alpha}{2}[/tex]
Here alpha is the angle [In radians] and r is the radius-
*First: We determine the angle:
[tex]\alpha=360-42-180\Rightarrow\alpha=138[/tex]
Now, we transform it to radians:
[tex]138\cdot\frac{\pi}{180}=\frac{23}{30}\pi[/tex]
*Second: We replace on the equation:
[tex]A=(6)^2\cdot\frac{(\frac{23}{30}\pi)}{2}\Rightarrow A=\frac{69}{5}\pi[/tex]
So, the area of the green sector is 69pi/5 square centimeters. [Approximately 43.4 square centimeters]
