Q. 154.3( 291 Votes )

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.


Answer :


As quadrant is 1/4 th of a circle and area of circle is Πr2
Area of quadrant =


=154 cm2


Area of triangle= 



= 7 × 14

= 98 cm2
In right angle triangle ABC,
BC2 = AB2 + AC2 
BC2 = (14)2 + (14)2 
 BC2 = 2(14)2
 BC= 14 √2 cm
Hence diameter is 14 √2 cm.
Radius is (14 √2)/2 = 7 √2 cm
So, area of the semicircle = 1/2 πr2

 


= 154 cm2


Area of segment BC = Area of semi-circle - Area of Triangle = 154 - 98 = 56cm2

Area of the shaded region = Area of semi Circle - Area of segment BC = 154 - 56

= 98 cm2

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