In trapezium \( \mathrm{ABCD}, \mathrm{AB} \| \mathrm{DC} \) and \( \mathrm{L} \) is the mid-poi...

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In trapezium \( \mathrm{ABCD}, \mathrm{AB} \| \mathrm{DC} \) and \( \mathrm{L} \) is the mid-point of \( \mathrm{BC} \). Through \( L \), a line \( P Q \| A D \) has been drawn which meets \( A B \) in \( P \) and \( D C \) produced in Q. Prove that \( \operatorname{ar}(\mathrm{ABCD})=\operatorname{ar}(\mathrm{APQD}) \)
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