Q) Find the area of the segment AYB shown in the figure, if the radius of the circle is 21 cm and angle AOB = 120⁰.

[Use π = 22/7]

(Q 27 – 30/2/2 – CBSE 2026 Question Paper)

Ans:

Step 1: From the diagram, we can see that the area of segment AYB

= Area of Sector AOBY – Area of Triangle AOB

Step 2:  Area of Sector AOBY = π r ²

= (21) ²

= x 21 x 21 = 22 x 21

= 462 cm²

Step 3: Area of Triangle = x OA x OB x sin 120⁰

= x 21 x 21 x

= 190.74 cm²

Step 4: Now, Area of Segment AYB

= Area of Sector AOBY – Area of Triangle AOB

= 462 – 190.74 = 271.26 cm²

Therefore, the area of Segment AYB is approx. 271.26 cm²

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