If the area of a triangle is $150 \, m^{2}$ and the ratio of the base and the height is $3:4$,then find its height in $m$.

$A$ 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?

The area of a square field is $6050\, m^2$. How much time will it take to reach from one of its corners to the opposite corner at the rate of $10\, m$ in every $30$ seconds?

$2$ poles of heights $15\, m$ and $30\, m$ stand upright on a playground. If their feet are $36\, m$ apart,find the distance between their tops in meters.

The area of the circumcircle of an equilateral triangle is $3 \pi \, cm^2$. The perimeter of the triangle is

In $\triangle ABC,$ a line parallel to side $BC$ intersects sides $AB$ and $AC$ at points $D$ and $E$ respectively. Point $D$ divides $AB$ in the ratio $1:4.$ If the area of $\triangle ABC$ is $200 \text{ cm}^2,$ what is the area (in $\text{cm}^2$) of quadrilateral $DECB$?