Question

the length of sides of a triangular field are 28 m, 15 m, 41 .calculate the area of the field.Find the cost of Levelling the field at the rate of
Rs.20 per meter square. ​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Area of the field is 126 m².

Cost of Leveling the field is Rs. 252.

Step-by-step explanation:

Given:

Let length of sides of a Triangle be,

a = 28 m

b = 15 m

c = 41 m

To Find:

Area of Triangle = ?

Cost of leveling the field at the rate of  Rs.20 per meter square = ?

Solution:

Area of a Triangle for sides  a ,b , c  is given by Heron's Formula as

$\textrm{Area of Triangle}=\sqrt{s(s-a)(s-b)(s-c)}$

Where,

$s = semi\ perimeter=\dfrac{a+b+c}{2}\\\\s=\dfrac{28+15+41}{2}=42\\\\s=42$

Substituting 's' in Heron's Formula we get,

$\textrm{Area of Triangle}=\sqrt{42(42-28)(42-15)(42-41)}$

$\textrm{Area of Triangle}=\sqrt{42(14)(27)(1)}=\sqrt{15876}=126\ m^{2}$

Now for Cost

Rate = Rs. 20 per meter square

Hence, for 126 meter square will be

$Cost=20\times 126=252$

Therefore,

Area of the field is 126 m².

Cost of Leveling the field is Rs. 252.