Answer :

Let r be the radius of each sector = 21 cm


Area of the shaded region = Area of the four sectors


Let angles subtended at A, B, C and D be x°, y°, z° and w° respectively.


Angle subtended at A, B, C, D (in radians, (θ)) be respectively.


Area of a sector with central angle at A =



Area of a sector with central angle at B



Area of a sector with central angle at C



Area of a sector with central angle at D



Area of four sectors =


Since, sum of all interior angles in any quadrilateral is 360°


x + y + z +w = 360°


Thus, Area of four sectors =



= 441π cm2


= 1386 cm2


Hence, required area of the shaded region is 1386 cm2.


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