Unless stated otherwise, use π=  $22/7 $

1.   Find the area of the shaded region in Fig. 12.19, if PQ = 24 $cm$, PR = 7 $cm$ and O is the centre of the circle.


  
    
      
    
	    
      
    
  

  
  
   
     
	 
	 

P
Q
R
O




  

 
2.   Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O
		are 7  $cm$ and 14  $cm$ respectively and ∠AOC = 40°.
		
 
   

    
		
	
	 	

  
  	
	

 
 
 


3.   Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14  $cm$ and
	APD and BPC are semicircles.
	
	







	

	
4.   Find the area of the shaded region in Fig. 12.22, where a circular arc of radius 6  $cm$ has been drawn with vertex O
	of an equilateral triangle OAB of side 12  $cm$ as centre.
	
		








5.   From each corner of a square of side 4  $cm$ a quadrant of a circle of radius 1  $cm$ is cut and also a circle of 
	diameter 2  $cm$ is cut as shown in Fig. 12.23. Find the area of the remaining portion of the square.
	
	
	
	
      
    
		
      
    
	
	
	
	
	
	
	
	
    
	
6.   In a circular table cover of radius 32  $cm$, a design  is  formed  leaving  an  equilateral triangle ABC in the middle
	as shown in Fig. 12.24. Find the area of the design.


7.   In Fig. 12.25,ABCD is a square of side 14  $cm$. With centres A, B, C and D, four circles are drawn such that each circle
	touch externally two of the remaining three circles. Find the area of the shaded region.
	
	
	
	
	
	
	
	
	
	
	
	
	

8.   Fig. 12.26 depicts a racing track whose left and right ends are semicircular.The distance between the two inner parallel
	line segments is 60 $m$ and they are each 106 $m$ long. If the track is 10 $m$ wide, find :
	
	(i)  the distance around the track along its inner edge
	
	(ii) the area of the track.
	
	
	
	
		
      
    
	
			
      
    
	
	
	
		
	

	

	
    

	
	

		
		

	

9.   In Fig. 12.27, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and  OD  is  the 
	diameter  of  the  smaller  circle.  If OA = 7  $cm$, find the area of the shaded region.
	
		
	
	
		
      
    
	
	

	
	
	
	
	
	
	
	
10.   The area of an equilateral triangle ABC is 17320.5 $cm^2$. With each vertex of the triangle as centre, a circle is drawn 
	with radius equal to half the length of the side of the triangle (see Fig. 12.28). Find the area  of  the  shaded  region.  (Use  π =  3.14  and
	(√3 = 1.73205)
	
	
    
	
	
	
    	
	
	
 

11.   On  a  square  handkerchief,  nine  circular  designs  each  of  radius  7   $cm$  are  made (see Fig. 12.29).
	  Find the area of the remaining portion of the handkerchief.


12.   In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5  $cm$. If OD = 2  $cm$, find the area of the
		(i)  quadrant OACB,                              (ii)  shaded region.
		
		
		
	
		
      
    
	
	

	
    
	
	
	O
	A
	B
	D
	C
	
	

		
		
13.   In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20  $cm$, find the area of the shaded region.
		(Use π= 3.14)
		
	
		
	
		
      
    
	
	

	
    
	
	
	O
	Q
	P
	A
	B
	C
	
	

		
 

14.   AB and CD are respectively arcs of two concentric circles of radii 21  $cm$ and 7  $cm$ and centre O (see Fig. 12.32). 
	If ∠AOB = 30°, find the area of the shaded region.
	
		
		
	
	
      
    
	
	

	
	
	
	

	
	
	O
	A
	B
	C
	D
	
	

		
	
15.   In Fig. 12.33, ABC is a quadrant of a circle of radius 14  $cm$ and a semicircle is drawn with BC as diameter.
		Find the area of the shaded region.
		
	
		
	
		
      
    
	
	
      
    
	
	
	
	
	
	

	
	
	A
	C
	B	
	

	
	

16.   Calculate  the  area  of  the    region  in Fig.common between the two quadrants of circles of 
		radius 8  $cm$ each.
		
		
		
		
		
		
		
		
		
		
	
		
		A
		B
		C
		D
		
        		
		


Solution