Question

What’s the area of the shaded region?

Answer 1

D

Explanation:

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

`r=√((x_2-x_1)^2+(y_2-y_1)^2)`

This implies that:

`r=\sqrt{(√(2)-0)^2+(-√(2)-0)^2}=2`

From the diagram;

`\cos(A)=(√(2) )/(2)`

`\implies A=45\degree`

Also;

`\cos(B)=(√(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

`(\theta)/(360\degree)* \pi r^2`

`=(165)/(360\degree)* \pi * 2^2`

`=(11)/(6)\pi`