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.

Explanation

Let ABCD be a parallelogram field with sides AB=CD=60m, BC=DA=40m and diagonal BD=80m.
`"Area of parallelogram" ABCD=2("Area of " triangleABD)`
`" In "triangleABD,`
`"Semi-perimeter of a triangle "triangleABD,`
`s=(a+b+c)/(2)`
`=(AB+BD+DA)/(2)`
=90 m
`therefore" ""Area of "triangleABD=sqrt(s(s-a)(s-b)(s-c))" "["by Heron's formula"]`
`=sqrt(90(90-60)(90-80)(90-40))`
`=sqrt(90xx30xx10xx50`
`=100xx3sqrt(15)=300sqrt15m^(2)`
From Eq. (i).
`"Area of parallelogram" ABCD=2xx300sqrt15=600sqrt15m^(2)`
`"Hence, the area of the parallelogram is " 600sqrt15m^(2)`.