In the figure given below, the radius of the circle is 42 cm. The angle in the sector is 60∘. What is the area of the major segment?
4620+441√3 sq. cm
Area of segment APB = Area of sector OAPB + Area of △OAB
Area of sector OAPB = Area of circle - Area of minor sector
=πr2−60360πr2=56πr2
△OAB is isosceles as OA = OB = radius. Hence, ∠OAB=∠OBA=θ
In △OAB, 60+θ+θ=180∘ [Angle Sum Property]
⇒θ=60∘
Thus, we can say that △ OAB is an equilateral triangle.
Area of the △ OAB = √34r2
Hence, area of segment APB = Area of sector OAPB + Area of △OAB
=56πr2+√34r2
=56×227×42×42+√34×42×42
=4620+441√3 sq. cm