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

A circle is inscribed in a rhombus with diagonals $12$ cm and $16$ cm. The ratio of the area of circle to the area of rhombus is

In a trapezium $\mathrm{ABCD}, \mathrm{AB}$ is parallel to $\mathrm{DC}, \mathrm{BC}$ is perpendicular to DC and $\angle \mathrm{BAD}=45^{\circ}$. If $\mathrm{DC}=5 \mathrm{~cm}, \mathrm{BC}=4 \mathrm{~cm}$, the area of the trapezium in sq cm is