Find the area of the sector of a circle of radius 14 cm and angle of sector is \(45^\circ\)

The correct choice is: 77 $\mathrm{cm}^2$

Area of sector $= \dfrac{\theta}{360^\circ} \times \pi r^2 = \dfrac{45}{360} \times \dfrac{22}{7} \times 14 \times 14 = \dfrac18 \times 616 = 77\ \mathrm{cm}^2$.

Hence the answer is 77 $\mathrm{cm}^2$.