The area of an equilateral triangle,each of whose sides measures $2 \sqrt{3} \text{ cm}$ is

If the ratio of the areas of two squares is $9: 1$,then the ratio of their perimeters is

$A$ wire,when bent in the form of a square,encloses a region of area $121 \, cm^2$. If the same wire is bent into the form of a circle,then the area of the circle is ........ $cm^2$. (Use $\pi = \frac{22}{7}$)

$A$ circular ground whose diameter is $35 \ m$ has a $1.4 \ m$ broad garden around it. What is the area of the garden in square metres?

$ABC$ is a triangle. $AB = 5 \text{ cm}$,$AC = \sqrt{41} \text{ cm}$,and $BC = 8 \text{ cm}$. $AD$ is perpendicular to $BC$. What is the area (in $\text{cm}^2$) of triangle $ABD$?

$ABCD$ is a cyclic quadrilateral. $AB$ and $DC$ when produced meet at $P$. If $PA = 8 \ cm$,$PB = 6 \ cm$,and $PC = 4 \ cm$,then the length (in $cm$) of $PD$ is: