In the given figure, O is the centre of the circle. ∠AOB = 90° and OA = 3 cm. Find the area of the shaded region.

Given: Radius of the circle = 3 cm and angle subtended by the arc = 90°

Area of the segment ARB = area of sector OARB – area of triangle OAB

We know that the area of the minor sector

⇒ Area of ABDC

⇒ Area of ABDC = 7.071428cm²

In ∆ABC,

∠A = 90°, AB = AC = 3 cm {radius of the circle}

∵ ∆ABC is a right angled triangle.

Area of ∆ABC

⇒ Area of ∆ABC

⇒ Area of ∆ABC = 4.5cm²

∴ Area of the segment BDC = area of sector ABDC – area of triangle ABC

⇒ Area of the segment BDC = 7.071428 – 4.5

⇒ Area of the segment BDC = 2.57cm²