Question 1019649
*[illustration pentagon3.pict]

No image was submitted, so I'm guessing this was the problem. 

The circle area is 

{{{pi(r^2)}}}

{{{pi(2^2)}}}

{{{4pi}}}

The hexagon has 6 triangles, all equilateral, with sides of 2. 

When we look at the single triangle we can drop a line and divide into 2 right triangles. The right triangle has a base of 1 and hypotenuse of 2. Pythagorus gives us {{{a^2+b^2=c^2}}}

Here, {{{H^2+1^2=2^2}}}

{{{H^2+1=4}}}

{{{H^2=3}}}

{{{H=sqrt(3)}}}

1/2bh gives us an area of  {{{sqrt(3)}}} as well. multiply this by 6 and total hexagon area is {{{6sqrt(3)}}}

The shaded area is {{{4pi-6sqrt(3)}}} or 2.174 sq cm