Bunuel wrote:

In the figure above, a circle with center O is inscribed in square ABCD. What is the total area of the shaded regions?

(A) 4 – π/2

(B) 8 – 2π

(C) 8 – 3π/2

(D) 16 – 4π

(E) 16 – 2π

Attachment:

2017-11-23_1215_002.png

Area of square minus circle yields 4 regions' area(Square area) - (Circle area) = area of

all 4 equal small corner regions

Square side length = \(4\)

Area of square = \(s^2 = 16\)

Square's side length = circle's diameter, \(d\) and \(d = 2r\)

\(4 = 2r\)

\(r = 2\)

Circle's area: \(πr^2 = 4π\)

(Square area) - (circle area)= Area of 4 regions= \(16 - 4π\)

2 of 4 regions are shaded

So if (Square area) - (circle area) = 4 regions

Then (Square area) - (circle area) divided by 2 = area of 2 regions

\(\frac{16 - 4π}{2}\) = 2 shaded regions

Shaded regions' area = \(8 - 2π\)

Answer B

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"