Advertisement Remove all ads

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

Sum

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]`

Advertisement Remove all ads

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 cm

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 18 Area of Circle, Sector and Segment
Exercise 18B | Q 48 | Page 835
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×