Question

ABCD is a quadrant of a circle of radius 14cm . with as diameter a semi-circle is drawn. Find the area of the shaded region​

Answer 1

Answer:

As ABC is a quadrant of the circle, ∠BAC will be of measure 90º.

In ΔABC, BC2 = AC2 + AB2 = (14)2 + (14)2 BC = 14√2

Radius (r1) of semi-circle drawn on BC = 14√2/2                                                                   =7√2  

Area of ΔABC = 1/2 AB x AC                        

=1/2 x 14 x 14                         =98 cm2  

Area of sector ABDC = 90o/360o  x π r2                                          = 1/4 x 22/7 x 14 x 14                                  

= 154 cm2

Area of semi - circle drawn on BC = Area of shaded region = Area of semi - circle -(Area of sector ABDC - Area of Trangle ABC)

=154-(154-98) =98 cm2

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