Question

Find the area of the segment AYB shown in figure, if radius of the circle is 21 cm and $<AOB={120}^0$. $\left(Use\pi =\frac{22}{7}\right)$

Answer 1

Given angle of arc = 120 degrees

radius of circle = 21 cm

Area of circle = π*r^2

=3.14*21*21

=1386 cm2

Area of Arc= (angle of arc/ 360)*area of circle

= (120 /360)*1386

=1386/3

=462 cm2

Area of triangle = a*b*sinx / 2

=21*21*sin(120) /2

=190.96 cm2

Area of segment = area of arc - area of triangle

=462 - 190.96

=271.04 cm2