Question

how to divide an equilateral triangle into three small triangles of equal areas

Answer 1

Draw a triangle ABC. Then draw its medians AD BE AND CF. Mark the point of intersection of all the three medians as O.
You will get Triangle ABO Triangle BOC & Triangle COA having equal areas.

In triangle ABC
taking median AD
area of triangle ABD = area of the triangle ACD
by median property

also in triangle BOC
as the median will be OD
thus area of triangle BOD= area of triangle COD
THUS NOW area of triangle ABD -area of triangle BOD = area of triangle ACD - area of triangle COD
THUS AREA OF TRIANGLES ABO = CAO
like this we will have to prove for all the medians and get three different results.

Answer 2

First you find the centroid or incentre or circumcentre because in case of equilateral triangle all these points are same so find circumcentre by perpendicular bisector of sides meet at a point is circumcentre ...And from this point join the all three vertices of triangle then u will find three triangle having equal areas...