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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.
Solution
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`.
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