In figure, arcs have been drawn with radii 14 cm each and with centers P, Q and R. Find the area of the shaded region.


Let r be the radius of each sector = 14 cm


Area of the shaded region = Area of the three sectors


Let angles subtended at P, Q, R be x°, y°, z° respectively.


Angle subtended at P, Q, R (in radians, (θ)) be respectively.


Area of a sector with central angle at P




Area of a sector with central angle at Q




Area of a sector with central angle at R =




Area of three sectors =


Since, sum of all interior angles in any triangle is 180°


x + y + z = 180°


Thus, Area of three sectors = = 308 cm2


Hence, the required area of the shaded region is 308 cm2.


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