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Answer:
The area of △AON is one-sixth part of △ABC.
Step-by-step explanation:
Let the total area of △ABC be x.
Median divides the area of a triangle in two equal parts.
Since AM are CN are medians, therefore the area of △ACN, △BCN, △ABM and △ATM are equal, i.e., .
The intersection point of medians is called centroid of the triangle. A centroid divides the median in 2:1.
Since CN is median and O is the centroid of the triangle, therefore CO:ON is 2:1.
Draw a perpendicular on CN from A.
Therefore the area of △AON is one-third of △ACN.
The area of ANO is . Therefore the area of △AON is one-sixth part of △ABC.
