ABCD is a rectangle of length 20cm and breadth 10cm.OAPB is a sector of a circle of radius 10√2cm. Calculate the area of the shaded region.[Takeπ=3.14]
Answers
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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