CAT (QA) PYQs

The sides $A B$ and $C D$ of a trapezium $A B C D$ are parallel, with $A B$ being the smaller side. $P$ is the midpoint of $CD$ and $ABPD$ is a parallelogram. If the difference between the areas of the parallelogram $ABPD$ and the triangle $BPC$ is $10$ sq cm, then the area, in sq cm, of the trapezium $A B C D$ is

In a parallelogram $ABCD$ of area $72 \mathrm{sq} \mathrm{cm}$, the sides $CD$ and $AD$ have lengths $9 \mathrm{~cm}$ and $16 \mathrm{~cm}$, respectively. Let P be a point on $C D$ such that $A P$ is perpendicular to $C D$. Then the area, in sq cm, of triangle $A P D$ is

The points $(2, 5)$ and $(6, 3)$ are two end points of a diagonal of a rectangle. If the other diagonal has the equation $y = 3x + c$, then $c$ is