Question

Find the area of minor segment of circle or radius 28 cm when the angle of corresponding sector is 45 degree

Answer 1

see the figure,

we have to find area of shaded region.

area of minor segment = area of minor sector - area of triangle OAB

= $\frac{\theta}{360^{\circ}}\times\pi r^2-\frac{1}{2}r^2sin45^{\circ}$

[ actually, I used the formula of area of triangle from properties of triangle. $\triangle=\frac{1}{2}absinC=\frac{1}{2}bcsinA=\frac{1}{2}casinB$, means area of triangle is half of products of consecutive sides of triangle and sine of angle between them ]

here, $\theta=45^{\circ},r=28cm$

now, area of minor segment = 45°/360° × 22/7 × 28 × 28 - 1/2 × 28 × 28 × 1/√2

=1/8 × 22 × 4 × 28 - 14 × 14√2

= 11 × 28 - 196√2

= 308 - 196√2

= 30.814 cm²

hence, area of minor segment is approximately 31 cm²