Bunuel wrote:

In the figure above, vertex R of square PQRS is the center of the circle. If QT = TR = 3, what is the area of the shaded region?

(A) 9 + 27π/4

(B) 9 + 27π

(C) 36 + 27π/4

(D) 36 + 9π

(E) 36 + 27π

Attachment:

2017-11-17_0948.png

We can consider the shaded region as the total area of a square and ¾ the area of a circle.

Since TR = 3, the radius of the circle is 3 and the side of the square is 6.

Thus:

Area of the square is 6 x 6 = 36.

3/4 of the area of the circle is 3/4 x π x 3^2 = 27π/4.

So, the area of the shaded region is 36 + 27π/4.

Answer: C

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