The sides of a triangle measure $20 \, cm$,$24 \, cm$,and $32 \, cm$. Find its semi-perimeter. (in $, cm$)

State whether each of the following statements is true or false:
$(1)$ In a square,if the length of each side is $20 \, cm$,then the length of its diagonal is $20 \sqrt{2} \, cm$.
$(2)$ If each side of an equilateral triangle is doubled,the area of the triangle is twice the area of the original triangle.

Area of a rectangle $=$ ............

The perimeter of a triangular field is $420\, m$ and its sides are in the ratio $6: 7: 8$. Find the area of the triangular field (in $m^2$).

$A$ field is in the shape of a trapezium having parallel sides $90 \, m$ and $30 \, m$. These sides meet the third side at right angles. The length of the fourth side is $100 \, m$. If it costs $\operatorname{Rs} 4$ to plough $1 \, m^2$ of the field,find the total cost of ploughing the field (in $\operatorname{Rs}$).

The diagonals of a rhombus are $16\,cm$ and $30\,cm$. Find its perimeter. (in $,cm$)