Cost of leveling a triangular plot at 20 paise per m^2:\nFind the total cost to level a triangle with sides 72 m, 30 m, and 78 m.

Introduction / Context:
Use Heron’s formula to compute the area from three sides, then multiply by the given rate (20 paise = Rs 0.20) to obtain cost.

Given Data / Assumptions:

• Sides: 72 m, 30 m, 78 m.
• Rate: 20 paise per m^2 = Rs 0.20 per m^2.

Concept / Approach:
Heron’s formula: with semiperimeter s = (a + b + c)/2, area Δ = √[s(s − a)(s − b)(s − c)]. Cost = area * 0.20.

Step-by-Step Solution:

Verification / Alternative check:
Right/acute check: sides satisfy triangle inequality; numerical square-root confirms an integer area 1080, making the rate multiplication exact.

Why Other Options Are Wrong:
Rs. 220, Rs. 200, Rs. 210, Rs. 224 differ from the exact multiplication of 1080 by Rs 0.20.

Common Pitfalls:
Treating 20 paise as Rs 20 or mixing units; or arithmetic mistakes in the product under the radical.

Final Answer:
Rs. 216