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Question
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]`
Solution
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"`
`=22/7(42)^2-1/2xx63xx72.66`
= 5544 - 2288.79
= 3255.21 cm2
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