The measurements of the sides of a triangle are $12 \, cm$,$17 \, cm$,and $25 \, cm$. Find the area of this triangle. (in $, cm^2$)

The sides of a triangle measure $15 \text{ cm}$,$17 \text{ cm}$,and $20 \text{ cm}$. Then,the semi-perimeter of the triangle is ......... $\text{cm}$.

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 $12 \, cm.$

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

For a plank in the shape of a parallelogram,the adjacent sides measure $12 \, cm$ and $17 \, cm$,and one of its diagonals measures $25 \, cm$. Find the cost of painting the plank at the rate of Rs. $3$ per $cm^2$.

Find the area of a triangular field,two sides of which are $510\,m$ and $520\,m$ and the perimeter is $1560\,m$. Also,find the cost of the field at the rate of Rs. $21$ per $m^2$.