A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What is the area of the circle ?

Solution (By Examveda Team)

$$\eqalign{ & 2\pi R = 2\left( {l + b} \right) \cr & \Rightarrow 2\pi R = 2(26 + 18)cm \cr & \Rightarrow R = \left( {\frac{{88}}{{2 \times 22}} \times 7} \right)cm \cr & \Rightarrow R = 14\,cm \cr} $$
∴ Area of the circle :
$$\eqalign{ & = \pi {R^2} \cr & = \left( {\frac{{22}}{7} \times 14 \times 14} \right)c{m^2} \cr & = 616\,c{m^2} \cr} $$