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]`

Answer 1

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