CAT (QA) PYQs

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

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s$. Then the area of triangle is

Let $D$ and $E$ be points on sides $A B$ and $A C$, respectively, of a triangle $A B C$, such that $A D: B D=2: 1$ and $A E: C E=2: 3$. If the area of the triangle $A D E$ is $8 \mathrm{sq} \mathrm{cm}$, then the area of the triangle $ABC$ , in sq cm , is