According to Heron's formula,the area of an equilateral triangle having each side $a$ is ..........

Write True or False and justify your answer.
The area of an equilateral triangle is $20 \sqrt{3} \text{ cm}^2$ whose each side is $8 \text{ cm}$.

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

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

The sides of a triangle are $a \, cm$,$b \, cm$,and $c \, cm$. Also,its semi-perimeter is $s \, cm$. If $s - a = 10 \, cm$,$s - b = 15 \, cm$,and $s - c = 12 \, cm$,then $s = \dots \, cm$.

The area of a trapezium is $475 \, cm^2$ and the height is $19 \, cm$. Find the lengths of its two parallel sides if one side is $4 \, cm$ greater than the other.