A circular lawn has an area of 154 m2. A path of 7 m width surrounds the lawn. What is the area of the lawn including the path? (in m²).

Explanation

Area of the lawn = $$\pi r^2 = 154$$ => $$\frac{22}{7} r^2 = 154$$ => $$r^2 = \frac{154 \times 7}{22} = 49$$ => $$r = \sqrt{49} = 7$$ Now, radius of lawn including path = 7 + 7 = 14 metre $$\therefore$$ Required area = $$\pi R^2$$ = $$\frac{22}{7} \times 14^2$$ = $$22 \times 28 = 616 m^2$$