1 of 4

AREAS RELATED

TO CIRCLE

Sum based on Area and

Perimeter of semicircle

2 of 4

Sol.

Radius (r₁) =

12 cm

∴

PQ

=

QR =

RS

4 cm

=

12

3

QS =

QR + RS

(4 + 4) cm

=

8 cm

P

Q

R

S

4cm

Diameter (PS)

6 cm

Q. PQRS is a diameter of a circle of radius 6 cm. The lengths PQ,

QR and RS are equal. Semi-circles are drawn on PQ and QS as

diameters as shown in given figure, Find the perimeter and area

of the shaded region.

=

∴

Diameter PS is divided

into three equal parts

=

PS

3

=

QS

∴

PQ

=

QR =

RS

3 of 4

Perimeter of shaded region =

circumference of semi-circle with diameter PS

+ circumference of semi-circle with diameter PQ

+ circumference of semi-circle with diameter QS

= π

=

Sol.

P

Q

R

S

4cm

(πr₁

=

+ πr₂

+ πr₃)

π(

r₂ = 2cm

r₁

+

r₂

+

r₃)

r₃ = 4cm

Perimeter of shaded region is 37.71cm

∴

+

2

+

4)

(6

22

7

=

×

12

264

7

=

= 37.71 cm

Q. PQRS is a diameter of a circle of radius 6 cm. The lengths PQ,

QR and RS are equal. Semi-circles are drawn on PQ and QS as

diameters as shown in given figure, Find the perimeter and area

of the shaded region.

What is the formula to find circumference of a semicircle ?

πr

4 of 4

Q. PQRS is a diameter of a circle of radius 6 cm. The lengths PQ,

QR and RS are equal. Semi-circles are drawn on PQ and QS as

diameters as shown in given figure, Find the perimeter and area

of the shaded region.

Area of shaded region =

Sol.

=

1

2

×

1

2

×

π (

=

1

2

×

22

7

=

264

7

=

P

Q

R

S

What is the formula to find area of a semicircle ?

=

1

2

1

2

+

1

2

1

2

–

(36 + 4 – 16)

1

2

×

22

7

=

×

24

ar(semi-circle with diameter PS)

6²

+ ar(semi-circle with diameter PQ)

– ar(semi-circle with diameter QS)

r₂ = 2cm

+ 2²

r₃ = 4cm

– 4²)

12

Area of shaded region is 37.71 cm²

∴

= 37.71 cm²