Area of a square $= (........... )^{2}.$

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 $12 \, cm.$

The sides of a triangle measure $12 \ cm$,$35 \ cm$,and $37 \ cm$. Find the area of the triangle. (in $cm^2$)

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are $13 \, m$,$14 \, m$,and $15 \, m$. The advertisements yield an earning of $Rs \, 2000$ per $m^2$ a year. $A$ company hired one of its walls for $6$ months. How much rent did it pay? (in $Rs$)

Find the area of the equilateral triangle having length of each side $50\, cm$.

The sides of a quadrilateral $ABCD$ are $6 \, cm$,$8 \, cm$,$12 \, cm$,and $14 \, cm$ (taken in order) respectively,and the angle between the first two sides is a right angle. Find its area in $cm^2$.