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Answer :
It can be observed that, \(\triangle{ADX}\) and \(\triangle{ACX}\) lie on the same base AX and are between the same parallels AB and DC.
\(\therefore \) Area (\(\triangle{ADX}\)) = Area (\(\triangle{ACX}\)) ...(i)
Also, \(\triangle{ADY}\) and \(\triangle{ACX}\) lie on the same base AC and are between the same parallels AC and XY.
\(\therefore \) Area (\(\triangle{ACY}\)) = Arca (\(\triangle{ACX}\)) ...(ii)
From Equations (i) and (ii), we get,
Area (\(\triangle{ADX}\)) = Area (\(\triangle{ACY}\))
Hence, proved.