$ABCD$ is a square. If $AC = 16 \, cm$,then find the area of $ABCD$ in $cm^2$.

$ABCD$ is a square. $E$ and $F$ are respectively the midpoints of $BC$ and $CD$. If $R$ is the midpoint of $EF$,prove that $\operatorname{ar}(\triangle AER) = \operatorname{ar}(\triangle AFR)$.

Observe the given figure. Does the parallelogram $ABCD$ and the triangle $QBC$ lie on the same base and between the same parallels? If yes,write the common base and the two parallels.

$ABCD$ is a parallelogram and $BC$ is produced to a point $Q$ such that $AD = CQ$. If $AQ$ intersects $DC$ at $P$,show that $\operatorname{ar}(BPC) = \operatorname{ar}(DPQ)$.

In which of the following figures,do you find two polygons on the same base and between the same parallels?

In parallelogram $XYZW$,$XY = 24 \, cm$. Altitudes $WP$ and $WQ$ are corresponding to bases $XY$ and $YZ$ respectively. If $WP = 6 \, cm$ and $WQ = 8 \, cm$,then find $YZ$ and the perimeter of parallelogram $XYZW$.