# Find the area of the shaded region given in figure - Mathematics

Sum

Find the area of the shaded region given in figure

#### Solution

Radius of one sector = r1 = 7 cm

Radius of second sector = r2 = 21 cm

Central angle of one sector = 120°

Central angle of second sector = 40°

Central angle of one sector (in radians) = θ1 = (120π)/180

Central angle of second sector (in radians) = θ2 = (40π)/180

Area of first sector = 1/2 r^2 theta_1

= 1/2 xx 49 xx (120pi)/180

= 1/2 xx 49 xx (120 xx 22)/(180 xx 7)

154/3 = 51.33  cm^2

Area of second sector = 1/2 r^2 theta_2

= 1/2 xx 441 xx (400pi)/180

= 1/2 xx 441 xx (40 xx 22)/(180 xx 7)

= 154 cm2

Let the lengths of the corresponding arc be l1 and l2.

Now, arc length of first sector = Radius × Central Angle (in radians)

= 7 xx (120pi)/80

= (7 xx 120 xx 22)/(180 xx 7)

= 44/3 cm

Now, arc length of second sector = Radius × Central Angle (in radians)

= 21 xx (40pi)/180

= (21 xx 40 xx 22)/(180 xx 7)

= 44/3 cm

Hence, we observe that arc lengths of two sectors of two different circles may be equal but their area need not be equal.

Concept: Areas of Sector and Segment of a Circle
Is there an error in this question or solution?

#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.4 | Q 17 | Page 135
Share