Question

3. Calculate the area of the shaded region.
10 cm
2 cm
2cm
2cm
2 cm
6 cm
16 cm
10 cm​

Answer 1

Answer:

Solution: Here, OR is the hypotenuse of △ABC,

because lines from two ends of diameter always make a right angle when they meet at circumference.

So, BC  

2

=AB  

2

+AC  

2

 

5  

2

+12  

2

 

= 25+144 = 169

= BC = 13

= Or, BC = 13cm Or radius = 6.5cm

Area of triangle =  

2

1

​  

 x base x height

=  

2

1

​  

 x 12 x 5

= 6 x 5

30 sq cm

Area of semicircle =  

2

1

​  

 x π r  

2

 

=  

2

1

​  

 x π x 6.5  

2

 

=  

2

1

​  

 x 3.14 x 42.25

=  

2

132.665

​  

 

= 132.665 sq. cm

area of shaded region = 132.665 - 30 = 102.665 sq. cm