The ratio of the measures of the sides of a triangle is $3: 4: 6$. If the semiperimeter of the triangle is $39 \, cm$,the measure of the longest side of the triangle is ............ $cm$.

How much paper of each shade is needed to make a kite as shown in the figure,where $ABCD$ is a square with diagonal $44 \, cm$? (in $cm^2$)

The shape of a field is a triangle. The measurements of the sides of the field are $51 \,m$,$52 \,m$ and $53 \,m$. Find its area. (in $,m^2$)

The sides of a triangle are $56 \ cm$,$60 \ cm$,and $52 \ cm$ long. Then the area of the triangle is (in $cm^2$)

An isosceles triangle has a perimeter of $84 \, cm$ and each of the equal sides is $30 \, cm$. Find the area of the triangle.

The dimensions of a rectangle $ABCD$ are $51 \, cm \times 25 \, cm$. $A$ trapezium $PQCD$ with its parallel sides $QC$ and $PD$ in the ratio $9:8$ is cut off from the rectangle as shown in the figure. If the area of the trapezium $PQCD$ is $\frac{5}{6}$ th part of the area of the rectangle,find the lengths $QC$ and $PD$.