Q11 of 47 Page 1

in fig. 4, O is the center of a circle such that diameter AB = 13 am and AC = 12 cm. BC is joined. Find the area of the shaded region. (Taken π = 3.14)

∠ACB = 90°


 


As angle in a semicircle is a right angle.


 


So △ABC is a right angled triangle


 


By Phythagoras theorem, which states, In a right angled triangle


 


(hypotenuse)2 = (base)2 + (perpendicular)2


 


In △ABC


 


AB2 = BC2 + CA2


 


132 = BC2 + 122


 


169 = BC2 + 144


 


BC2 = 25


 


BC = 5 cm


 


And we know,


 



 



 



 


= 30 cm2


 



 



 



 



 


= 66.3325 cm2


 


Area of shaded region = area of semicircle - Area of △ABC


 


= 66.3325 - 30


 


= 36.3325 cm2


 

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