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.