Question

the given figure, ΔABC is a right angled triangle in which ∠ A = 90°. Semicircles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.

Answer 1

Answer:

In △ABC,∠A=90

o

By Pythagoras theorem,

BC

2

=AB

2

+AC

2

BC

2

=3

2

+4

2

9+16=25

∴BC=5cm

A(shadded region)=A(△ ABC)+A (semicircle AB) + (semicircle AC) - A(semicircle BAC)

=

2

1

×3×4+

2

1

×π(

2

3

)

2

+

2

1

×π(

2

4

)

2

−

2

1

×π(

2

5

)

2

=6+

8

9π

+2π−

8

25π

=6+2π−2π

=6cm

2