Question

What’s the area of the shaded region?

Answer 1

Answer:

D

Step-by-step explanation:

Use the distance formula to find the radius of the circle.

$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

This implies that:

$r=\sqrt{(\sqrt{2}-0)^2+(-\sqrt{2}-0)^2}=2$

From the diagram;

$\cos(A)=\frac{\sqrt{2} }{2}$

$\implies A=45\degree$

Also;

$\cos(B)=\frac{\sqrt{3} }{2}$

$\implies B=30\degree$

The central angle of the shaded region is $\theta=30+90+45=165\degree$

The area of the shaded region is

$\frac{\theta}{360\degree}\times \pi r^2$

$=\frac{165}{360\degree}\times \pi \times 2^2$

$=\frac{11}{6}\pi$