Question

Question 6
A field in the form of a parallelogram has sides 60m and 40m and one of its diagonals is 80m long. Find the area of the parallelogram.

Answer 1

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 $\Delta ABD$) ….(i)
Consider $\Delta ABD$,
Semi – perimeter of a triangle $\Delta ABD$,
$s=\frac{a+b+c}{2}$
$=\frac{AB+BD+DA}{2}$
$=\frac{60+80+40}{2}=\frac{180}{2}$
$=90m$
$\therefore$ Area of $\Delta ABD=\sqrt{s(s-a)(s-b)(s-c)}$ [by Heron’s formula].
$=\sqrt{90(90-60)(90-80)(90-40)}$
$=\sqrt{90\times 30\times 10\times 50}$
$=100\times 3\sqrt{15}=300\sqrt{15}{m}^2$
From Eq.(i),
Area of parallelogram $ABCD=2\times 300\sqrt{15}=600\sqrt{15}{m}^2$
Hence, the area of the parallelogram is $600\sqrt{15}{m}^2$