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 perimeter of a square is double the perimeter of a rectangle. The area of the rectangle is $240 \, cm^2$. What is the area of the square? (in $cm^2$)

The area of a sector of a circle of radius $5 \, cm$,formed by an arc of length $3.5 \, cm$,is ..... $cm^2$.

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 $₹ 2.5$?

If the radius of one circle is $12$ times the radius of another,how many times does the area of the greater circle contain the area of the smaller circle?

The cost of fencing a circular plot at the rate of $Rs. 15$ per $m$ is $Rs. 3300$. What will be the cost of flooring the plot at the rate of $Rs. 100$ per square metre? (in $Rs.$)