The cost of laying the carpet is ₹ 10/m². Find the cost of laying carpet on a triangular field having sides 10m, 20m & 20m.

Concept used:

Area of a triangle using herons formula

Formula used:

Area of Δ = \(\sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} \)

S = Sum of three sides/2

Here, s is semi-perimeter and a, b, and c are the sides of the triangle.

Given:

The different sides of the triangle are 10 m, 20 m, and 20 m 

The cost of laying carpet at the rate of ₹ 10/m²

Calculation:

a = 10 m, b= 20 m, c = 20 m

Using Heron's formula,

s = \(\frac{10+20+20}{2}\) = 25m

Area of Δ = \(\sqrt {25(25-10)(25-20)(25-20)}\) = 25 √15   

The cost of laying carpet = The area of  Δ ABC × Rate of laying carpet 

= 25 √15 × 10 m²

= ₹ 250 √15

∴ The cost of laying carpet on a triangular field having sides 10m, 20m & 20m is ₹ 250 √15