1 of 6

AREAS RELATED

TO CIRCLE

  • Sum based on finding

Area of shaded region

2 of 6

A

D

B

C

Q. Find the area of the shaded region in adjacent figure,

if ABCD is a square of side 14 cm and

APD and BPC are semicircles.

Sol.

14 cm

Side of the square =

ar (shaded region) =

–

2 ar (semi-circles)

ar (◻ ABCD)

What is the formula to find area of a square?

(Side)2

(side)2

ar (◻ ABCD) =

(14)2

=

196 cm2

=

∴

ar (◻ ABCD) =

196 cm2

✔

14 cm

P

P

3 of 6

Q. Find the area of the shaded region in adjacent figure,

if ABCD is a square of side 14 cm and

APD and BPC are semicircles.

Sol.

ar (shaded region) =

–

ar (◻ ABCD)

✔

2 ar (semi-circles)

ar (◻ ABCD) = 196 cm2

What is the formula to find area of semi-circle?

?

1

2

 

πr2

Diameter = 14 cm

Radius (r) = 7 cm

∴

✔

2 ar (semi-circles)

2

×

=

1

2

× πr2

=

22

7

×

7

×

7

=

22

×

7

=

154 cm2

2 ar (semi-circles)

∴

✔

D

B

C

P

P

14 cm

A

4 of 6

Q. Find the area of the shaded region in adjacent figure,

if ABCD is a square of side 14 cm and

APD and BPC are semicircles.

Sol.

ar (shaded region) =

–

ar (◻ ABCD)

2 ar (semi-circles)

Ar (◻ ABCD) = 196 cm2

✔

✔

ar(shaded region) =

–

ar (◻ ABCD)

2 ar(semi-circles)

✔

A

D

B

C

P

P

14 cm

=

196

–

2 Ar (semi-circles) = 154 cm2

​

154

=

42 cm2

∴

Area of the shaded portion is 42 cm2

5 of 6

Q. On a square handkerchief, nine circular designs each of radius

7cm are made. Find the area of the remaining portion of the

handkerchief.

Sol.

radius of one circle

=

7 cm

Area of one circle

=

πr2

22

7

 

7

 

7

=

154 cm2

=

Side of square

=

=

42 cm

∴

 

14

14

 

14

Area of square

=

(side)2

=

(42)2

=

1764 cm2

ar(remaining portion) =

?

ar(◻ABCD)

What is formula to find area of square?

(side)2

A

B

C

D

?

Side of square =

Sum of diameter of 3 circles

∴ Diameter = 14 cm

14 cm

14 cm

14 cm

42 cm

What is formula to find area of circle?

πr2

✔

22

 

7

=

Area of 9 circles

=

∴

 

154

9

= 1386 cm2

– ar(nine circles)

?

✔

Area of square

∴

∴

Area of one circle

6 of 6

Q. On a square handkerchief, nine circular designs each of radius

7cm are made. Find the area of the remaining portion of the

handkerchief.

Sol.

Area of the remaining

portion

∴

=

ar (9 Circles)

–

ar (◻ABCD)

=

1386

–

1764

∴

Area of the remaining portion

is

378 cm2

A

B

C

D

42 cm

✔

✔

=

1764 cm2

ar ( ◻ABCD)

1386 cm2

ar (9 circles)

=

ar(remaining portion) =

ar(◻ABCD)

– ar(9 circles)

Area of the remaining

portion

∴

=

378 cm2