Question

MATHEI
16. In the given figure, O is the centre of a semi-circle
and AO I BC. If AB = 772 cm, then the area of
-
22
the shaded region is Use =
7
A
B
O
C​

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