Question

Find the cost of levelling a triangular piece of land measuring 80 m, 41 m and 41 m, if the rate is ₹ 12 per m².

Answer 1

Given:

• Sides of the triangular land: 80 m, 41 m and 41 m
• Rate of leveling land = ₹ 12 per m²

Step 1: Calculate the semi-perimeter (s) of the triangle.

`S = (80 + 41 + 41)/2`

= `162/2`

= 81 m

Step 2: Use Heron’s formula to find the area of the triangle.

Heron’s formula for area (A):

`A = sqrt(s(s - a)(s - b)(s - c))`

where a = 80, b = 41 and c = 41.

Calculate:

`A = sqrt(81(81 - 80)(81 - 41)(81 - 41))`

= `sqrt(81 xx 1 xx 40 xx 40)`

= `sqrt(129600)`

A = 360 m²

Step 3: Calculate the cost of leveling the land.

Cost = Area × Rate

= 360 × 12

= ₹ 4320

The cost of leveling the triangular piece of land is ₹ 4320.