The length of one pair of opposite sides of a square is increased by $5 \, cm$ on each side,the ratio of the length and the breadth of the newly formed rectangle becomes $3:2$. What is the area of the original square? (in $cm^2$)

The diameter of a circular wheel is $7\, m$. How many revolutions will it make in travelling $22\, km$?

In trapezium $ABCD$,$AB || CD$ and $AB = 2 \, CD$. Its diagonals intersect at $O$. If the area of $\Delta AOB = 84 \, cm^2$,then the area of $\Delta COD$ is equal to (in $cm^2$)

If the area of a triangle whose base is $6\, cm$ is equal to the area of a circle of radius $6\, cm$,then find the height of this triangle (in $cm$).

Each side of a rhombus is $26 \ cm$ and one of its diagonals is $48 \ cm$ long. The area of the rhombus is (in $cm^2$)

The smallest side of a right-angled triangle is $8\, cm$ less than the side of a square of perimeter $56\, cm$. The second largest side of the right-angled triangle is $4\, cm$ less than the length of the rectangle of area $96\, cm^2$ and breadth $8\, cm$. What is the largest side of the right-angled triangle? (in $cm$)