CAT (QA) PYQs

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

Let $ABCD$ be a parallelogram such that the coordinates of its three vertices $A, B, C$ are $(1, 1), (3, 4)$ and $(-2, 8)$, respectively. Then, the coordinates of the vertex $D$ are

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