The area of a right-angled triangle with base $6\,m$ and hypotenuse $6.5\,m$ is........$m^2$

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:

If the circumference of a circle is equal to the perimeter of a square,what is the ratio of the area of the circle to the area of the square?

Two circles touch each other externally. The sum of their areas is $130 \pi \text{ cm}^2$ and the distance between their centres is $14 \text{ cm}$. The radius of the smaller circle is . . . . . . $\text{cm}$.

$A$ circular road runs around a circular garden. If the difference between the circumference of the outer circle and the inner circle is $44\, m$,then find the width of the road in $m$.

Perimeter of a square and an equilateral triangle is equal. If the diagonal of the square is $12 \sqrt{2} \text{ cm}$,then find the area of the equilateral triangle.