$2$ 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 radius of the wheel of a vehicle is $70\, cm$. The wheel makes $10$ revolutions in $5\, seconds$. The speed of the vehicle is......$km/h$.

What would be the cost of laying a carpet on a floor which has its length and breadth in the respective ratio of $32:21$ and where its perimeter is $212$ feet,if the cost per square foot of laying the carpet is $₹ 2.5$?

$A$ circle and a rectangle have the same perimeter. The sides of the rectangle are $18 \, cm$ and $26 \, cm$. What is the area of the circle? (in $cm^2$)

$A$ wire is in the form of a semi-circle of $7 \, cm$ radius. The length of the wire will be (in $cm$):

In the given figure,$PQR$ is a triangle and quadrilateral $ABCD$ is inscribed in it. Given $QD = 2 \text{ cm}$,$QC = 5 \text{ cm}$,$CR = 3 \text{ cm}$,$BR = 4 \text{ cm}$,and $PB = 6 \text{ cm}$. What is the area (in $\text{cm}^2$) of the quadrilateral $ABCD$?