A rectangular lawn whose length is twice of its breadth is extended by having four semi-circular portions on its sides. What is the total cost (in ₹) of levelling the entire lawn at the rate of ₹100 per square metre, if the smaller side of the rectangular lawn is 12m? (Take π = 3.14)

85,320

We know that,

Area of rectangle = Length × Breadth 

Area of semi-circle = \(\frac{1}{2}\) × πr²

We have,

Length = 2 × Breadth

Breadth = 12m

Length = 2 × Breadth

Length = 2 × 12 = 24 m

Area of rectangle = Length × Breadth =  12 × 24 = 288 m²

Area of semi-circle on larger side = \(\frac{1}{2}\) × π × 12² = 72π m²

Area of semi-circle on smaller side = \(\frac{1}{2}\) × π × 6² =  18π m²

Total area of lawn = Area of rectangle + 2 × Area of semi-circle on larger side + 2 × Area of semi-circle on smaller side

= 288 + (2 × 72π ) + (2 × 18π)

= 288 + 2π(72 + 18)

= 288 + 2 × 3.14 × 90

= 288 + 565.2 = 853.2 m²

Total cost of levelling = Total area of lawn × 100

= 853.2 × 100 = 85320