The diagonals of a rhombus are $40 \, cm$ and $42 \, cm$. Find its area in $cm^2$.

From a point in the interior of an equilateral triangle,perpendiculars are drawn on the three sides. The lengths of the perpendiculars are $14 \, cm$,$10 \, cm$,and $6 \, cm$. Find the area of the triangle.

In a trapezium $ABCD$, $AB \parallel CD$. If $AB = 30 \, cm$, $BC = 17 \, cm$, $CD = 20 \, cm$, and $DA = 9 \, cm$, then find its area. (in $cm^2$)

In parallelogram $ABCD$,$AB = 9 \, cm$,$BC = 10 \, cm$ and $AC = 17 \, cm$,then find its area. (in $, cm^2$)

The sides of a triangle are $35 \text{ cm}$,$54 \text{ cm}$,and $61 \text{ cm}$,respectively. The length of its longest altitude 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 $8 \text{ cm}$.