$D$ 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 $BDEC$?

The dimensions of a field are $20 \text{ m}$ by $9 \text{ m}$. $A$ pit $10 \text{ m}$ long,$4.5 \text{ m}$ wide and $3 \text{ m}$ deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of the field as a result of this operation? (in $m$)

$A$ circular swimming pool is surrounded by a concrete wall $4 \ m$ wide. If the area of the concrete wall surrounding the pool is $11/25$ that of the pool,then the radius (in $m$) of the pool is

The area of a right-angled triangle with base $6\,m$ and hypotenuse $6.5\,m$ is........$m^2$

Find the perimeter (in $cm$) of a semicircle of radius $28\, cm$.

The length and breadth of a rectangular field are in the ratio $5: 3.$ If the cost of cultivating the field at $25$ $paise$ per square metre is ₹ $6000,$ then find the dimensions of the field.