Question

In a quadrilateral field sides are 8.5 m,8.5m,16.5m and 14.3m respectively and one diagonal is 15.4m . Find the cost of turfing it at the rate of ₹1.50 per m^2

Answer 1

Answer:

The total cost of turfing will be Rs 181.0.35

Step-by-step explanation:

Let's consider

a = 8.5 m

b = 8.5 m

c = 16.5 m

d = 14.3 m

and e = 15.4 m

Since we have given the measurements of four sides and one diagonal of the quadrilateral, so its divide it into two triangles.

One triangle having side a = 8.5 m b = 8.5 m and  e = 15.4 m and another triangle having side c = 16.5 m d = 14.3 m and e = 15.4 m

So, the semi-perimeter of first triangle is

$s\ =\ \dfrac{a+b+e}{2}$

  $=\dfrac{32.4}{2}$

   = 16.2

So, the area of triangle can be given by using heron's formula

$A_1\ =\ \sqrt{s(s-a)(s-b)(s-e)}$

    $=\ \sqrt{16.2(16.2-8.5)(16.2-8.5)(16.2-15.4)}$

   $=\ \sqrt{16.2(7.7)(7.7)(0.8)}$

    $=\ 27.72\ m^2$

Semi-perimeter of second triangle

$s\ =\ \dfrac{16.5+14.3+15.4}{2}$

   = 23.1

So, the area of triangle can be given by using heron's formula

$A_2\ =\ \sqrt{s(s-c)(s-d)(s-e)}$

  $=\ \sqrt{23.1(23.1-16.5)(23.1-14.3)(23.1-15.4)}$

  $=\ \sqrt{23.1(6.6)(8.8)(7.7)}$

    $=\ 97.59\ m^2$

$\textrm{So, total area of quadrilateral }=\ A_1\ +\ A_2$

                                                             $=\ 120.69\ m^2$

Since, price of turfing is Rs 1.50 per meter square

So, the total cost of turfing will be Rs. 1.5 x 120.69 =Rs 181.0.35