Cost of Road Construction Outside Square Field

Side of square $s = 200/4 = 50\text{ ft}$. Distance from center to corner = $\frac{50\sqrt{2}}{2} = 25\sqrt{2}\text{ ft}$. To construct a road outside the square field, inner radius $r = 25\sqrt{2}\text{ ft}$. Outer radius $R = 25\sqrt{2} + 7\sqrt{2} = 32\sqrt{2}\text{ ft}$.

Area of circular road = $\pi (R^2 - r^2) = \pi [(32\sqrt{2})^2 - (25\sqrt{2})^2] = \pi [2048 - 1250] = 798\pi\text{ sq.ft.}$ Taking $\pi = \frac{22}{7}$, Area = $798 \times \frac{22}{7} = 2508\text{ sq.ft.}$

Area of $50\%$ road = $2508 / 2 = 1254\text{ sq.ft.}$ Cost = $1254 \times 100 =$ Rs. $125,400$.