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

Let ABCD be a parallelogram field with sides AB = CD = 60 m, BC = DA = 40 m and diagonal BD = 80 m.

Area of parallelogram ABCD = 2(Area of ΔABD)  ...(i)

In ΔABD,

Semi-perimeter of a triangle ΔABD,

`s = (a + b + c)/2`

= `(AB + BD + DA)/2`

= `(60 + 80 + 40)/2`

= `180/2`

= 90 m

∴ Area of ΔABD = `sqrt(s(s - a)(s - b)(s - c))`  ...[By Heron’s formula]

= `sqrt(90(90 - 60)(90 - 80)(90 - 40))`

= `sqrt(90 xx 30 xx 10 xx 50)`

= `100 xx 3sqrt(15)`

= `300sqrt(15)  m^2`

From equation (i),

 Area of parallelogram ABCD = `2 xx 300sqrt(15) = 600sqrt(15)  m^2`

Hence, the area of the parallelogram is `600sqrt(15)  m^2`.