The area of a rectangle is $460 \, m^2$. If the length is $15 \%$ more than the breadth,what is the breadth of the rectangular field? (in $metres$)

In the figure,$DE \parallel BC$. If $DE = 3 \text{ cm}$,$BC = 6 \text{ cm}$,and the area of $\Delta ADE = 15 \text{ cm}^2$,then the area of $\Delta ABC$ is ............ $\text{cm}^2$.

$A$ rectangular paper,when folded into two congruent parts,has a perimeter of $34\, cm$ for each part when folded along one set of sides and a perimeter of $38\, cm$ when folded along the other set of sides. What is the area of the original paper in $cm^2$?

$A$ playground has the shape of a rectangle with two semi-circles on its smaller sides as diameters,added outside. If the sides of the rectangle are $36 \, m$ and $24.5 \, m$,then the area of the playground is ......... $m^2$ (use $\pi = \frac{22}{7}$).

In the given figure, $ABCDEF$ is a regular hexagon whose side is $6\, cm$. $APF$, $QAB$, $DCR$, and $DES$ are equilateral triangles. What is the area (in $cm^2$) of the shaded region (in $\sqrt{3}$)?

$A$ General,while arranging his men,who were $6000$ in number,in the form of a square,found that there were $71$ men leftover. How many were arranged in each row?