Bunuel wrote:

In the figure above, B is the center of the circle with radius 6. What is the area of the shaded region?

(A) 9π

(B) 36 – 9π

(C) 36π – 18

(D) 18 – 9π/2

(E) 9π – 18

Attachment:

2017-11-17_0947_003.png

The area of the shaded region =

(Sector area) - (triangle area)

Sector central angle = 90°

Sector = \(\frac{90}{360} =\frac{1}{4}\) circle area

Circle area = \(\pi*r^2 = 36\pi\)

Sector area: \(\frac{36\pi}{4}=9\pi\)

Right isosceles triangle area:

\(\frac{s^2}{2}=\frac{6^2}{2}=18\)

Shaded region's area =

(Sector area) - (triangle area)

\(9\pi - 18\)

Answer E

*OR

Area = \(\frac{b*h}{2}=\frac{6*6}{2}=\frac{36}{2}=18\)
_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"