What’s the area of the shaded region?

Question

asked Sep 11, 2020 219k views

1 Answer

Cody Casterline · Answer 1 · 2020-09-16T08:54:57+0000

Answer:

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

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

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

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