An equilateral triangle is inscribed in a circle, as shown above. What is the area of the shaded region, if the area of the circle is 2?  Choose one
A) 2 - 3√3  B) 2 - 3√3/∏  C) 2 - 3√3/4  D) 2 - 3√3/(2∏)  E) 2∏ - 3√3/(2∏)
1) since we are subtracting from overall so first term should be 2... E out   2) the area of triangle that is to be subtracted should be in terms of π...A and C are out.. also A gives you answer in negative   3) in B, ans would be around 0.3 and in D, ans will be around 1.2...   Clearly the shaded and unshaded are close to 1/2 each..   2 - 3√3/(2∏) is the answer
<result>D</result>
An equilateral triangle is inscribed in a circle, as shown above. What is the area of the shaded region, if the area of the circle is 2?