The area of an equilateral triangle is $9 \sqrt{3} \ m^{2}$. The length (in $m$) of the median is

In the given figure,triangle $ABC$ is drawn such that $AB$ is tangent to a circle at point $A$. The radius of the circle is $10 \, cm$. The line segment $BC$ passes through the center $O$ of the circle,and point $C$ lies on the circle. If $BC = 36 \, cm$ and $AB = 24 \, cm$,what is the area (in $cm^{2}$) of triangle $ABC$?

The perimeter of a square is double the perimeter of a rectangle. The area of the rectangle is $240 \, cm^2$. What is the area of the square? (in $cm^2$)

$A$ wire is looped in the form of a circle of radius $28\, cm$. It is bent again into a square form. What will be the length of the diagonal of the largest square possible thus?

$A$ rectangular park is $65\, m$ long and $50\, m$ wide. Two cross paths,each $2\, m$ wide,are to be constructed parallel to the sides. If these paths pass through the centre of the rectangle and the cost of construction is ₹ $17.25$ per $m^2$,then find the total cost involved in the construction (in ₹).

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