What is the perimeter of an equilateral triangle whose area is $4 \sqrt{3} \text{ cm}^2$?

$D$ and $E$ are points on sides $AB$ and $AC$ of $\Delta ABC$. $DE$ is parallel to $BC$. If $AD:DB = 2:3$,what is the ratio of the area of $\Delta ADE$ to the area of quadrilateral $BDEC$?

$A$ vessel is in the form of a hollow cylinder mounted on a hemispherical bowl. The diameter of the hemisphere is $14 \, cm$ and the total height of the vessel is $13 \, cm$. Find the capacity of the vessel in $cm^3$. (Take $\pi = 22/7$)

In the given figure,there is a large semicircle with diameter $AB = 56 \ cm$. Inside this,there are four smaller identical semicircles with diameters $AE, EF, FG,$ and $GB$ along the diameter $AB$. $A$ circle is inscribed such that it is tangent to the large semicircle and the two middle smaller semicircles. What is the area (in $cm^2$) of the shaded region?

$A$ cow is tied by a rope at the corner of a rectangular field. If the length of the rope is $14\, m$,then the area of the field which the cow could graze is.......$m^2$

$A$ parallelogram has sides $60\, cm$ and $40\, cm$ and one of its diagonals is $80\, cm$ long. Its area is