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.