$(1)$ Area of a rhombus $= \frac{1}{2} \times \ldots \ldots \ldots$
$(2)$ Area of a triangle $= \ldots \ldots \ldots$

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

If each side of a triangle is doubled,then find the ratio of the area of the new triangle thus formed to the area of the given triangle.

There is a slide in a park. One of its side walls has been painted in some colour with a message "$KEEP$ $THE$ $PARK$ $GREEN$ $AND$ $CLEAN$". If the sides of the wall are $15 \, m$,$11 \, m$ and $6 \, m$,find the area painted in colour.

$A$ kite in the shape of a square with a diagonal $32\, cm$ and an isosceles triangle of base $8\, cm$ and sides $6\, cm$ each is to be made of three different shades as shown in the figure. How much paper of each shade has been used in it?

If the sides of a triangular field are $290 \, m$,$290 \, m$,and $400 \, m$,find the area of the field in $m^2$.