CAT 2022 Slot 3 QA Question 3: 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

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

Accepted Answer

Since BD and CE are medians, D is the midpoint of AC and E is the midpoint of AB. Also, O is the centroid.
Triangle ACE has half the area of triangle ABC because E is the midpoint of AB.
$	ext{Area}(ACE) = \dfrac{108}{2} = 54$
In triangle ACE, D is the midpoint of AC, so triangle ECD has half the a