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 $cm$).

If the area of an equilateral triangle is $16 \sqrt{3} \, cm^{2}$,then the perimeter of the triangle is (in $cm$)

According to Heron's formula,the area of a triangle $=$ ...........

The diagonals of a rhombus are $16\,cm$ and $30\,cm$. Find its perimeter. (in $,cm$)

State whether each of the following statements is true or false:
$(1)$ If the side of an equilateral triangle is $10 \, cm,$ then its semi-perimeter is $30 \, cm.$
$(2)$ In an isosceles triangle,the length of two equal sides is $20 \, cm,$ then its semi-perimeter is $20 \, cm.$
$(3)$ In $\Delta ABC,$ $\angle B = 90^{\circ},$ $AB = 6 \, cm$ and $BC = 8 \, cm,$ then its semi-perimeter is $12 \, cm.$

Find the area of the triangle with the side lengths $51 \, cm$,$52 \, cm$,and $101 \, cm$. (in $, cm^2$)