circles

Since the central angle of the sector is 30^o,

     the area of the sector of the circle is 30^o / 360^o  = 1/12^th the area of the circle: 

                pi·r²/12  =  pi·6²/12

To find the area of the triangle, use the formula: 

                Area  =  ½·a·b·sin(C)  =  ½·r·r·sin(C)  =  ½·6·6·sin(30^o)

 

Thus, the answer is:  pi·6²/12  -  ½·6·6·sin(30^o)