# Easy Geometry & Mensuration Solved QuestionAptitude Discussion

 Q. A chord $AB$ of a circle of radius 5.25 cm makes an angle of $60^\circ$ at the centre of the circle. Find the area of the major segment.
 ✖ A. 168 cm$^{2}$ ✖ B. 100 cm$^{2}$ ✔ C. 84 cm$^{2}$ ✖ D. 70 cm$^{2}$

Solution:
Option(C) is correct

The given circle is an equivlateral triangle

Area of the minor sector

$=\dfrac{60}{360}\times \pi\times 5.25^2$

$=14.4375\text{ cm}^2$

Area of the triangle

$=\dfrac{\sqrt{3}}{4}\times 5.25^2$

$=11.93\text{ cm}^2$

Area of the minor segment = Area of the minor sector - Area of the triangle

$=2.5\text{ cm}^2$

Area of the major segment = Area of the circle - Area of the minor segment

$=86.54\text{ cm}^2-2.5\text{ cm}^2$

$84\text{ cm}^2$

## (1) Comment(s)

Prabhat
()

area of major sigment =area of triangle+ area of major sector

=11.93 cm2 + 300/360[π×(5.25)2]

= 11.93+72.1

=84 cm2