Question

A field in the form of a parallelogram has sides 60
m and 40 m and one of its diagonals is 80 m long.
Find the area of the parallelogram.​

Answer 1

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)