Question

In figure, 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 1

Answer:

Area of shaded region=area of semicircle of diameter BC-{area of quadrant of radius AB/AC- area of △ABC}

∵ BC is hypotenuse of right angle △ABC

here AB=BC=14

So, BC=14

2

=2×radius⇒radius=7

2

So, Area of semicircle of diameter BC=

2

πr

2

=

2

1

×

7

22

×(7

2

)

2

=154cm

2

Area of quadrant of radius AB/AC=

4

πr

2

=

4

1

×

7

22

×14×14

=154cm

2

Area of △ABC=

2

1

×h×b

=

2

1

×14×14=98cm

2

Now, area of shaded region=154−{154−98}=98cm

2

Hence, area of shaded region=98cm

2