Question

The diagonal of a field in the form of a quadrilateral are 106 m and 80 m and intersect each other ar right angles. Find the cost of cultivating the field at the rate of Rs. 25.50 per 100 m^2.

Answer 1

here is it




Considering parallelogram as two symmetrical triangles with sides 40,60,80 metres
we have 
Area of triange= Sqrt(s(s-40)(s-60)(s-80))
s=(40+60+80)/2=90
So area= Sqrt(90*(90-40)*(90-60)*(90-80))
=Sqrt(90*50*30*10)
=300*Sqrt(15)
Since there are two such triangle
Total area of parallelogram =2*300*Sqrt(15)
=600*Sqrt(15) m^2
Therefore the answer is 6)

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Answer 2

since diagonals intersect each other at right angle hence this quadrilateral will be a rhombus
so the area of rhombus
$= \frac{1}{2 } \times diagonal1 \times diagonal2 \\ = \frac{1}{2} \times 106 \times 80 \\ = 4240 \: square \: metre \\ \\ \: \: \: \: \: cost \\ = 4240 \times 25.50 \div 100 \\ = 108,1.20 \: rupees$