The base of a triangular field is three times its altitude. If the cost of cultivating the field at $50$ per hectare is $Rs. 675$,then what are its base and height?

If the perimeter of an isosceles right triangle is $(6+3 \sqrt{2}) \text{ m}$,then the area of the triangle is ... $\text{m}^2$.

The area of a trapezium is $2500 \, m^2$. One of its parallel sides is $75 \, m$. If the distance between the two parallel sides is $40 \, m$,then find the length of the other parallel side in $m$.

$A$ silver wire when bent in the form of a square,encloses an area of $484 \, cm^{2}$. Now if the same wire is bent to form a circle,the area enclosed by the circle would be? (in $cm^{2}$)

$A$ person $A$ takes $15 \text{ seconds}$ to cross a rectangular field diagonally walking at a speed of $52 \text{ m/min}$. $A$ person $B$ takes the same time to cross the same field along its sides (length + width) walking at a speed of $68 \text{ m/min}$. The area of the field is $....... \text{ m}^2$.

Mid-points of a triangle containing sides $12 \, cm$,$18 \, cm$,and $26 \, cm$ are joined to each other. Find the area of the triangle formed by joining the mid-points.