If the length of a rectangle is increased in the ratio $6:7$ and its breadth is diminished in the ratio $5:4$,then its area will be changed in the ratio:

The area of the incircle of an equilateral triangle of side $42 \ cm$ is (in $cm^2$)

Height of an equilateral triangle is $6 \, cm$. Find its side? (in $cm$)

The area of a circle is same as the area of a square. What is the ratio of the diameter of the circle and the diagonal of the square?

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

$A$ field is in the shape of a parallelogram. Its adjacent sides and one diagonal are $65 \, m$,$119 \, m$,and $156 \, m$ respectively. Find the cost of gravelling it at the rate of $₹ 10$ per $m^2$ (in $Rs.$).