In rhombus $ABCD$,$AC = 12 \, cm$ and $BD = 15 \, cm$,then $\operatorname{ar}(ABCD) = \dots \, cm^2$.

$AC$ is one of the diagonals of quadrilateral $ABCD$. $BM$ and $DN$ are altitudes on $AC$ from $B$ and $D$ respectively. If $AC = 18 \, cm$,$BM = 10 \, cm$,and $DN = 6 \, cm$,then $ar(ABCD) = \dots \dots \, cm^2$.

In the figure,if parallelogram $ABCD$ and rectangle $ABEM$ are of equal area,then:

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 $XYZW$.

If the mid-points of the sides of a quadrilateral are joined in order,prove that the area of the parallelogram so formed will be half of the area of the given quadrilateral.

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