Question

in the given figure ABC is an equilateral triangle . Two semi- circles with center O and P are drawn on sides AC and DC respectively as diameters . Find sum of the area of triangle ADC and the two semicircles​

Answer 1

Step-by-step explanation:

In △ABC,∠A=90

o

By Pythagoras theorem,

BC

2

=AB

2

+AC

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

6π

+2π−

8

25π

=6+2π−2π

=6cm

2