Answer: Option C
To find the cost of turfing the field, we need to calculate its area. Since the field is a quadrilateral, we can divide it into two triangles and calculate the area of each triangle using Heron's formula.
Heron's formula states that the area of a triangle with sides a, b, and c is given by:
$A = \sqrt{s(s-a)(s-b)(s-c)}$
where $s$ is the semi-perimeter of the triangle, given by:
$s = \frac{1}{2}(a+b+c)$
Using this formula, we can calculate the area of each triangle, and then add them to get the total area of the field. The semi-perimeter of the first triangle ABC is:
$s_1 = \frac{1}{2}(8.5 + 8.5 + 15.4) = 16.2$
Using Heron's formula, we get:
$A_1 = \sqrt{16.2(16.2-8.5)(16.2-8.5)(16.2-15.4)} \approx 53.57 \text{ m}^2$
Similarly, the semi-perimeter of the second triangle CDA is:
$s_2 = \frac{1}{2}(14.3 + 16.5 + 15.4) = 23.1$
Using Heron's formula, we get:
$A_2 = \sqrt{23.1(23.1-14.3)(23.1-16.5)(23.1-15.4)} \approx 91.17 \text{ m}^2$
The total area of the field is:
$A = A_1 + A_2 \approx 144.74 \text{ m}^2$
Therefore, the cost of turfing the field at the rate of Rs 1.50 per sq. metre is:
Cost = $1.50 \times A \approx Rs 194.04$
Hence, the correct answer is option C.If you think the solution is wrong then please provide your own solution below in the comments section .