goodyear2013 wrote:

Attachment:

Drawing.png

What is the area of the shaded region, formed by the intersection of an equilateral triangle with area √3, and an inscribed circle, as shown above?

A. √3 -3π

B. √3 - (4/3)π

C. (3√3) / 4

D. √3 - π/3

E. 3√3 - π

Is the formula for circle inscribed in the triangle the best way to solve this question?

The question is not as difficult as it looks but under time pressure,chances are you will get it wrong

Area of Eq. Triangle =\(\sqrt{3}\)/4*a^2=\(\sqrt{3}\) where a is the side of the triangle

Solve for "a" and we get a=2

Now radius of the circle is nothing but the radius of in circle. Radius of in circle for a equilateral triangle is given by

r=\(\sqrt{3}/6\) *a

or \(r=\frac{1}{\sqrt{3}}\)

Area of the shaded region: Area of Triangle - Area of circle

\(\sqrt{3}\)- π/3

Ans is D

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