Question

31. In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and Z BOD = 90°.
Find the area of the shaded region. (use it = 3.14)
​

Answer 1

Answer:

Area of the shaded region = area of the circle −area of the triangle ABC−area of the quadrant COD

Here, in triangle ABC ∠CAB=90

o

(angle in a semicircle)

Hence triangle ABC is right-angled at A

Then applying Pythagoras theorem,

BC

2

=AC

2

+AB

2

BC

2

=24

2

+7

2

BC

2

=625

BC=25 cm

Therefore diameter of circle =25cm

i.e., Radius=

2

25

=12.5 cm

Then area of circle =πr

2

=490.625 cm

2

Area of triangleABC=

2

1

×base×height

=84 cm

2

Area of quadrant =

4

1

×πr

2

=122.65625 cm

2

Therefore area of shaded region =490.625−84−122.65625=283.96875 cm

2

Answer 2

Answer:

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