Question

ABCD is a rectangle of length 20cm and breadth 10 cm. OAPB is a sector of a circle of radius 10 root 2 cm. Calculate the area of the shaded region.

Answer 1

Answer:

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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