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 parallelogram $ABCD$ has area $48 \mathrm{sqcm}$. If the length of CD is $8 \mathrm{~cm}$ and that of $AD$ is s cm , then which one of the following is necessarily true?

A park is shaped like a rhombus and has area $96$ sq m. If $40$ m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of $125$ per m, is