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

$A$ triangle and a parallelogram have the same area. If the sides of the triangle are $10 \, cm$,$17 \, cm$,and $21 \, cm$,and the parallelogram stands on the base $12 \, cm$,find the height of the parallelogram. (in $, cm$)

The area of an equilateral triangle with each side measuring $16\,cm$ is how many times the area of an equilateral triangle with each side measuring $8\,cm$?

Find the area of the trapezium $PQRS$ given in the figure.

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 a triangle whose sides are $33 \, cm$,$34 \, cm$,and $65 \, cm$. (in $, cm^2$)