Find the area of the shaded region in Fig., if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠ AOC = 40°.

We know that,  formula for the area of the sector of a circle

Area of the sector = $\frac{\theta }{{360}^0}$ $\times$ ${\mathrm{\pi r}}^2$

Where, r is the radius and $\theta$ be the angle at the center

and $\theta$ = 40⁰

Consider that, 

The radius of the bigger circle = R = OA = 14 cm

The radius of the smaller circle = R = OB = 7 cm

Thus, by observing the above diagram we get

Area of shaded region ABDC = Area of sector ACO - Area of sector BDO

= θ/360⁰ $\times$ $\mathrm{\pi }$R² - θ/360⁰ $\times$ $\mathrm{\pi }$r²

= θ/360⁰$\mathrm{\pi }$ (R² - r²)

= θ/360⁰ $\mathrm{\pi }$ (R $+$ r )(R $-$ r)

= 40⁰/360⁰ $\times$  22/7 $\times$ (14 $+$ 7) (14 $-$ 7)

= 1/9 $\times$ 22/7 $\times$ 21 $\times$ 7

= (22 $\times$ 21 $\times$ 7)/(9 $\times$ 7) 

= (22 $\times$ 7)/3

= 154/3 cm²