Question

33.
ABCD is a rectangle of length 20 cm and breadth 10 cm. OAPB is a sector
of a circle of radius 1002 cm. Calculate the area of the shaded region.
| Take n = 3.14]
20 cm​

Answer 1

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Answer 2

Given : ABCD is a rectangle of length 20 cm and breadth 10 cm. OAPB is a sector  of a circle of radius 10√2 cm

To find  :  area of the shaded region.

Solution:

Area of Rectangle =   20 * 10 = 200  cm²

OA = OB =10√2

AB = 20 cm

AB² = OA² + OB²  

=> OAB is right angle triangle at O

=> ∠AOB = 90°

Area of Sector OAB = (90/360) π (10√2)²

= (1/4)(3.14) 200

=   157 cm²

Area of Δ OAB  = (1/2) * OA * OB = (1/2) * 10√2 * 10√2 = 100 cm²

area of the shaded region. = area of rectangle + area of Triangle OAB - area of Sector OAPB

= 200 + 100 - 157

= 143 cm²

area of the shaded region. = 143  cm²

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