A circular arc of radius

6 cm
has been drawn with vertex of an equilateral triangle of side

12 cm
as center and a sector of circle of radius

6 cm
with center

B
is made. The area of the shaded region is ____

cm
2

.

[Use
3

=1.73 and π=3.14.]

Question

A circular arc of radius

6 cm
   has been drawn with vertex of an equilateral triangle of side

12 cm
   as center and a sector of circle of radius

6 cm
  with center

B
   is made. The area of the shaded region is ____

cm
    2

.

[Use
    3
   
   =1.73 and π=3.14.]

Accepted Answer

A circular arc of radius 6 cm has been drawn with vertex of an equilateral triangle of side 12 cm as center and a sector of circle of radius 6 cm with center B is made. The area of the shaded region is 137.64 cm2.We know that,Radius is 6cm and the vertex of the equilateral triangle is 12cm.Draw the figure:Area of equilateral triangle =

3

4
   
   ×
    
     ( side )
    2

Now, area of equilateral triangle

ΔAOB
  is-

=

3

4
       
       ×
        
         (AB)
        2

=
        
         1.73
        4

(12)
        2

=62.28 
        
         cm
        2

Area of sector of a circle having an angle

θ

=
    θ
    
     360
   
   π
    r
    2

where,

r
   is the radius of the circle and

θ
   is the sector angle. And, area of sector having central angle 60° is-

=
        
         60
        
         360
       
       ×
        
         22
        7
       
       ×
        6
        2

=
        1
        6
       
       ×3.14×36

=18.84 
        
         cm
        2

Also, area of sector having central angle

360
      °
     
     −
      
       60
      °

is-

=
        
         300
        
         360
       
       ×
        
         22
        7
       
       ×
        6
        2

=
        5
        6
       
       ×3.14×36

=94.2 
        
         cm
        2

Therefore, area of the shaded region is-= (Area of

ΔAOB
  − Area of sector having central angle 60°) + Area of sector having central angle (360° − 60°)

=62.8−18.84+94.2

=137.64 
        
         cm
        2

Hence, the area of the shaded region is 137.64

cm
    2

.

A circular arc of radius $6 c m$ has been drawn with vertex of an equilateral triangle of side $12 c m$ as center and a sector of circle of radius $6 c m$ with center $B$ is made. The area of the shaded region is ____ $cm 2$ . $[Use 3 =1 . 73 and π =3 . 14 .]$

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A circular arc of radius 6 cm has been drawn with vertex of an equilateral triangle of side 12 cm as center and a sector of circle of radius 6 cm with center B is made. The area of the shaded region is ____ cm 2 . [Use 3 =1.73 and π=3.14.]