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 $\sqrt{3}$)?

The circumference of a circular field is $440 \, m$. $A$ circular path of $10 \, m$ width runs around the outside of the field. Find the cost of gravelling the path at the rate of $70 \, \text{paise}$ per square metre? (in $Rs.$)

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 $metres$)

The area of the incircle of an equilateral triangle of side $42 \ cm$ is (in $cm^2$)

$A$ 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?

$A$ circle and a rectangle have the same perimeter. The sides of the rectangle are $18 \, cm$ and $26 \, cm$. What is the area of the circle? (in $cm^2$)