CAT (QA) PYQs

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

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

A circle of diameter $8$ inches is inscribed in a triangle ABC where $\angle A B C=90^{\circ}$. If $B C=10$ inches then the area of the triangle in square inches is