Explanation

(d)
If $p_{1}$ and $p_{2}$ be the distance between parallel sides and $\theta$ be the angle between adjacent sides, then
Required area $= p_{1}p_{2}\ cosec\ \theta$
$Where,\ p_{1} = \frac{1}{\sqrt{\left( 1 + m^{2} \right)}},\ p_{2} = \frac{1}{\sqrt{\left( 1 + n^{2} \right)}}$
(distance between parallel lines)
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$and\ \tan\theta = \frac{|m - n|}{|1 + mn|}\$
$\therefore$ Required area
$= \frac{1}{\sqrt{(1 + m^{2})\sqrt{(1 + n^{2})}}} \bullet \frac{\sqrt{{(1 + m}^{2})}\sqrt{(1 + n^{2})}}{|m - n|}$
$= \frac{1}{|m - n|}$