Question

In figure ABC is a right-angled triangle in which ZA=90°, AB=21 cm and AC=28 cm. Semi-circles are
described on AB, BC, and AC as diameters. Find the area of the shaded region.
А
B
C​

Answer 1

Answer:775.25−481.25=294cm  

Step-by-step explanation:

Area of shaded region = ar. semi-circle AB + ar. semi-circle AC + ar. △ABC - ar. semi-circle BC

=  

2

π

​  

[r  

1

2

​  

+r  

2

2

​  

]+  

2

1

​  

×AB×AC−  

2

π

​  

×r  

3

2

​  

 

=  

2

1

​  

×  

7

22

​  

[(  

2

21

​  

)  

2

+(  

2

28

​  

)  

2

]+  

2

1

​  

×21×28−  

2

1

​  

×  

7

22

​  

×(  

2

BC

​  

)  

2

 

=  

7

11

​  

[  

4

441

​  

+  

4

784

​  

]+294−  

7

11

​  

×[  

4

AB  

2

+AC  

2

 

​  

]

=  

7

11

​  

×  

4

1225

​  

+294−  

7

11

​  

×  

4

1

​  

[21  

2

+28  

2

]=775.25−  

28

11

​  

×1225

=775.25−481.25=294cm  

2