Median am and cn of △abc intersect at point o. what part of area of △abc is the area of △aon?

The area of △AON and the area of △ABC is x. The area of △AON is one-sixth part of △ABC.

Step-by-step explanation:

Let the total area of △ABC be x.

A median of a triangle 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., .

A centroid is the intersection point of all medians of a triangle. A centroid divides each 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 as shown in below figure. Let the height of the pendicular on CN from A be h.

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.