1 of 4

AREAS RELATED

TO CIRCLE

  • Sum based on finding area of

shaded portion

2 of 4

  1. ABC is a quadrant of a circle of radius 14 cm and a

semicircle is drawn with BC as diameter.

Find the area of the shaded region.

A

C

B

Q

14 cm

14 cm

Sol.

In ΔABC,

BC2

AB2 + AC2 =

= BC2

∴

+ (14)2

196 + 196

∴

BC2 =

[By Pythagoras theorem]

2 × 196

∴

BC2 =

BC =

∴

 

Area of shaded region =

– ar(minor segment)

ar(semi-circle)

?

P

What is formula to find area of semi-circle?

 

To find: R

∠A= 90o

(14)2

?

 

?

3 of 4

  1. ABC is a quadrant of a circle of radius 14 cm and a

semicircle is drawn with BC as diameter.

Find the area of the shaded region.

A

C

B

Q

14 cm

14 cm

Sol.

Radius of semi-circle =

=

BC

2

 

2

=

 

Area of shaded region =

– ar(minor segment)

ar(semi-circle)

?

P

To find: R

BC is diameter of semi-circle

7

1

2

 

22

7

 

 

 

 

Area of semi-circle

=

=

154 cm2

=

11

1

2

×

πR2

∴

Radius of semi-circle

 

11

 

 

 

 

=

∴

Area of semi-circle

✔

∴

77

 

2

=

4 of 4

  1. ABC is a quadrant of a circle of radius 14 cm and a

semicircle is drawn with BC as diameter.

Find the area of the shaded region.

A

C

B

Q

14 cm

14 cm

Sol.

Area of shaded region =

ar(semi-circle)

?

✔

 

– ar(minor segment)

154 cm2

=

Area of semi-circle

– ar(ΔABC)

P

ar(A – BPC)

7

90

360

 

22

7

 

14

 

14

ar (A – BPC ) =

=

154 cm2

=

4

2

2

θ

360

 

πr2

22

 

7

=

∴

ar (A – BPC )

?

✔

What is formula to find area of sector?