$D$ 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 $BDEC$?

What is the area of a given right-angled triangle?
$I.$ The length of the hypotenuse is $5\, cm$.
$II.$ The perimeter of the triangle is four times that of its base.
$III.$ One of the angles of the triangle is $60^{\circ}$.

In $\Delta ABC$,$AD$ and $AE$ are bisectors of $\angle BAC$ and $\angle BAD$ respectively. If $\angle BAE = 30^{\circ}$,$AE = 9 \text{ cm}$,and $EC = 15 \text{ cm}$,what is the area (in $\text{cm}^2$) of $\Delta AEC$?

In a shower,$10\, cm$ of rain falls. What will be the volume of water that falls on $1$ hectare area of ground? (in $m^3$)

The volume of a cube is $216 \, cm^3$. Part of this cube is then melted to form a cylinder of length $8 \, cm$. Find the volume of the cylinder (in $cm^3$)?

In the given figure,circle $P$ has a diameter of $2 \ m$ and circle $Q$ has a diameter of $1 \ m$. Find the area of the shaded region.