$ABCD$ is a rhombus. If $AC = 16 \, cm$ and $BD = 30 \, cm$,then find the area of $ABCD$ in $cm^2$.

The mid-points of the sides of a triangle along with any of the vertices as the fourth point make a parallelogram of area equal to:

In the given figure,$ABCD$ is a trapezium with $AB \parallel DC$. $E$ is a point on extended $BC$. Prove that $ar(BDE) = ar(ACED)$.

The median of a triangle divides it into two:

In parallelogram $PQRS$,$PQ = 15 \, cm$. Altitudes $SM$ and $SN$ are corresponding to bases $PQ$ and $QR$ respectively. If $SM = 6 \, cm$ and $SN = 10 \, cm$,find $QR$ and the perimeter of $PQRS$.

In the figure,$CD \parallel AE$ and $CY \parallel BA$. Prove that $\operatorname{ar}(\triangle CBX) = \operatorname{ar}(\triangle AXY)$.