There are 4 semi-circular gardens on each side of a square-shaped pond with each side 21 m. The cost of fencing the entire plot at the rate of ₹ 12.50 per metre is

### Concept & Perimeter of Composite Shapes When semi-circles are attached to the outside of a square, the "fencing" of the entire plot only covers the outer boundary (the curved arcs). The straight sides of the square are internal and not fenced. $$ \text{Perimeter} = 4 \times (\text{Arc length of semi-circle}) $$ ### Step-by-Step Solution * Given: Side of the square pond $a = 21$ m. This acts as the diameter ($d$) of each semi-circular garden. * The outer boundary consists of 4 semi-circular arcs. * The arc length of one semi-circle is $\frac{\pi d}{2} = \frac{1}{2} \times \frac{22}{7} \times 21 = \frac{1}{2} \times 66 = 33$ m. * Total perimeter for 4 such semi-circles is $4 \times 33 = 132$ m. * The cost of fencing is ₹ 12.50 per metre. * Total cost $= 132 \times 12.50$. * Calculation trick: $132 \times \frac{25}{2} = 66 \times 25 = 1650$. ### Exam Strategy & Shortcut Four semi-circles of diameter $d$ form exactly two full circles. The perimeter is simply $2 \times \pi d = 2 \times \frac{22}{7} \times 21 = 132$ m. Cost = $132 \times 12.5 = 1650$. This saves computing fractional arc lengths. ### Common Pitfall The most frequent error is calculating the area instead of the perimeter, or unnecessarily adding the sides of the inner square to the perimeter, which leads to overestimating the fencing cost. ### Final Answer Therefore, the correct answer is **₹ 1650**.