In figure, arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilateral ABCD as centers. Find the area of the shaded region.
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.