Ex 12.3, 4
Find the area of the shaded region in figure, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.
Area of shaded region
= Area of circle with radius 6 cm
+ Area of equilateral triangle with side 12 cm
β Area of sector ODE
Area of circle
Radius of circle = r = 6 cm
Area of circle = πr2
= 22/7Γ(6)2
= 22/7 Γ 36
= 792/7 cm2
Area of equilateral triangle
Area of equilateral triangle = β3/4 (side)2
= β3/4Γ(12)^2
= β3/4Γ12Γ12
= β3Γ3Γ12
= 36β3 cm2
Area of sector ODE
Radius = r = 6 cm ,
& ΞΈ = β DOE = 60Β°
Area of sector OCD = ΞΈ/360Γππ2
= (β DOπΈ)/360Γππ2
= (60Β°)/(360Β°)Γ22/7Γ62
= 1/6Γ22/7Γ6Γ6
= 22/7Γ6
= 132/7
Now,
Area of shaded region
= Area of circle with radius 6 cm
+ Area of equilateral triangle with side 12 cm
β Area of sector ODE
= 792/7+36β3 β132/7
= (792 + 7 Γ 36β(3 )β 132)/7
= (792 + 252β3 β 132)/7
= (660 + 252β3)/7
= 660/7 + (252β3)/7
= (660/7 +36β3) cm2
Hence, area of shaded region = (660/7+36β3) cm2

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.