Unless stated otherwise, use π=  $\frac{22}{7}$

1.   Find the area of the shaded region in Fig. 12.19, if PQ = 24 $\mathit{c}\mathit{m}$, PR = 7 $\mathit{c}\mathit{m}$ and O is the centre of the circle.


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


3.   Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14  $\mathit{c}\mathit{m}$ 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  $\mathit{c}\mathit{m}$ has been drawn with vertex O
	of an equilateral triangle OAB of side 12  $\mathit{c}\mathit{m}$ as centre.
	
		

5.   From each corner of a square of side 4  $\mathit{c}\mathit{m}$ a quadrant of a circle of radius 1  $\mathit{c}\mathit{m}$ is cut and also a circle of 
	diameter 2  $\mathit{c}\mathit{m}$ 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  $\mathit{c}\mathit{m}$, 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  $\mathit{c}\mathit{m}$. 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 $\mathit{m}$ and they are each 106 $\mathit{m}$ long. If the track is 10 $\mathit{m}$ 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  $\mathit{c}\mathit{m}$, find the area of the shaded region.
	
		
	
10.   The area of an equilateral triangle ABC is 17320.5 $\mathit{c}{\mathit{m}}^2$. 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   $\mathit{c}\mathit{m}$  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  $\mathit{c}\mathit{m}$. If OD = 2  $\mathit{c}\mathit{m}$, find the area of the
		(i)  quadrant OACB,                              (ii)  shaded region.
		
			
		
13.   In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20  $\mathit{c}\mathit{m}$, find the area of the shaded region.
		(Use π= 3.14)
		
		
 

14.   AB and CD are respectively arcs of two concentric circles of radii 21  $\mathit{c}\mathit{m}$ and 7  $\mathit{c}\mathit{m}$ and centre O (see Fig. 12.32). 
	If ∠AOB = 30°, find the area of the shaded region.
	
			
	
15.   In Fig. 12.33, ABC is a quadrant of a circle of radius 14  $\mathit{c}\mathit{m}$ and a semicircle is drawn with BC as diameter.
		Find the area of the shaded region.
		
	
	

16.   Calculate  the  area  of  the    region  in Fig.common between the two quadrants of circles of 
		radius 8  $\mathit{c}\mathit{m}$ each.
		
		


Solution