Question

2. Find the area of the shaded region : 4 cm A7 cm + 12 cm​

Answer 1

Let radius is r.

Perimeter =2r+2πr×43

                 =2r+722×r×23

                 =2r+733r=47

                 747r=47    ,  r=7 cm

Area =πr2×43

         =722×72×43=115.5cm2 

Answer 2

Answer:

Class 10

>>Maths

>>Areas Related to Circles

>>Areas of Combinations of Plane Figures

>>Find the area of a shaded region in the

Question

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Find the area of a shaded region in the given figure, where a circular arc of radius 7 cm has been drawn with vertex A of an equilateral triangle ABC of side 14 cm as centre. (Use π =

7

22

and

3

=1.73).

973617

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Medium

Solution

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⇒ Here, Radius of circle r=7cm

⇒ Area of circle =πr

2

=

7

22

×(7)

2

=154cm

2

⇒ Side of equilateral triangle is 14cm.

⇒ Area of equilateral triangle =

4

3

×(side)

2

⇒ Area of equilateral triangle =

4

3

×(14)

2

⇒ Area of equilateral triangle =

4

1.73

×196=84.87cm

2

⇒ ∠A=60

o

[ Angle of equilateral triangle ]

∴ θ=60

o

⇒ Area of sector =

360

o

θ

×πr

2

⇒ Area of sector =

360

o

60

o

×

7

22

×(7)

2

∴ Area of sector =25.66cm

2

⇒ Area of shaded region = (Area of circle + Area of equilateral triangle ) - 2×Area of sector

⇒ Area of shaded region =(154+84.87)−51.32=187.55cm

2

Step-by-step explanation:

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