Answer:
D
Step-by-step explanation:
Use the distance formula to find the radius of the circle.
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This implies that:
[tex]r=\sqrt{(\sqrt{2}-0)^2+(-\sqrt{2}-0)^2}=2[/tex]
From the diagram;
[tex]\cos(A)=\frac{\sqrt{2} }{2}[/tex]
[tex]\implies A=45\degree[/tex]
Also;
[tex]\cos(B)=\frac{\sqrt{3} }{2}[/tex]
[tex]\implies B=30\degree[/tex]
The central angle of the shaded region is [tex]\theta=30+90+45=165\degree[/tex]
The area of the shaded region is
[tex]\frac{\theta}{360\degree}\times \pi r^2[/tex]
[tex]=\frac{165}{360\degree}\times \pi \times 2^2[/tex]
[tex]=\frac{11}{6}\pi[/tex]
