Question

Suppose the medians BD and CE of a triangle ABC intersect at a point O. If area of triangle ABC is 108 sq. cm, then, the area of the triangle EOD, in sq. cm, is

Answer 1

$\text{Area of} \ △ABD:\text {Area of} \ △BDC =1:1$
Thus, Area of $△ABD$ $= 54$
$\text{Area of} \ △EDB:\text {Area of} \ △ADE =1:1$.
Thus, the area of $△ADE=27$
As a result, the O is the centroid, which divides the medians in $2\ratio1$.
$\text{Area of} \ △BEO:\text {Area of} \ △EOD =2:1$.
Now, the area of $△EOD=9$

So, the answer is $9$ sq cm.