Area of a rectangle $=$ ............

In the figure,$\Delta ABC$ has sides $AB = 7.5\, cm$,$AC = 6.5\, cm$,and $BC = 7\, cm$. On base $BC$,a parallelogram $DBCE$ of the same area as that of $\Delta ABC$ is constructed. Find the height $DF$ of the parallelogram (in $cm$).

$A$ rectangular plot is given for constructing a house, having a measurement of $40 \, m$ long and $15 \, m$ in the front. According to the laws, a minimum of $3 \, m$ wide space should be left in the front and back each, and $2 \, m$ wide space on each of the other sides. Find the largest area where the house can be constructed (in $m^2$).

In $\Delta ABC$,$AB = 6 \, cm$,$BC = 8 \, cm$,and $AC = 10 \, cm$. $BM$ is an altitude on $AC$. Then $BM = \dots \, cm$.

The shape of a field is a triangle. The measurements of the sides of the field are $51 \,m$,$52 \,m$ and $53 \,m$. Find its area. (in $,m^2$)

Find the area of a triangle,two sides of which are $15\,cm$ and $28\,cm$ and the perimeter is $84\,cm$. (in $,cm^2$)