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On a Circular Table Cover of Radius 42 Cm, a Design is Formed by a Girl Leaving an Equilateral Triangle Abc in the Middle, as Shown in the Figure. Find the Covered Area of the Design.V - Mathematics


On a circular table cover of radius 42 cm, a design is formed by a girl leaving an equilateral triangle ABC in the middle, as shown in the figure. Find the covered area of the design. `["Use" sqrt(3) = 1.73, pi =22/7]`

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Construction:  Join AO and extend it to D on BC.

Radius of the circle, r = 42 cm
∠OCD= 30° 

cos30° `= "DC"/"OC"`

`=> sqrt(3)/2 = "DC"/42`

`⇒ "DC" = 21sqrt(3)`

`=> "DC" = 2xx"DC" = 42sqrt(3) = 72.66  "cm"` 

sin 30°`="OD"/"OC"`

`=>  1/2="OD"/42`

⇒ OD = 21 cm

Now, AD = AO + OD = 42 + 21  = 63 cm

Area of shaded region =  Area of circlec - Area of triangle ABC

`= pi(OA)^2-1/2xx"AD"xx"AB"`


= 5544 - 2288.79

= 3255.21 cm

  Is there an error in this question or solution?
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RS Aggarwal Secondary School Class 10 Maths
Chapter 18 Area of Circle, Sector and Segment
Exercise 18B | Q 48 | Page 835
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