Question

ABC is a right-angled triangle, with right angle at B. If the semi-circle on AB as
diameter encloses an area of 81 sq cm and the semi-circle on BC as diameter encloses
an area of 36 sq cm, then area of the semi-circle on AC, with AC as radius (in sq cm)
will be :​

Answer 1

Answer:

Step-by-step explanation:

Given ∠B=90

∘

,AB=28cm,BC=21cm

Area of shaded region=ar△ABC+area of semicircle AC-ar quarter circle BC

=

2

1

​

×BC×AB+

2

1

​

×π(

2

AC

​

)

2

−

4

1

​

×π(BC)

2

=[

2

1

​

×21×28]+[

2

1

​

×

7

22

​

×

4

1

​

(

28

2

+21

2

​

)

2

]−

4

1

​

×

7

22

​

×21×21

=294+[

28

11

​

×1225]−346.5

=294+481.25−346.5=428.75㎠