If a wire is bent into the shape of a square,then the area of the square is $81 \, cm^2$. When the wire is bent into a semi-circular shape,the area of the semi-circle will be (in $cm^2$):

The sides of a right-angled triangle forming the right angle are in the ratio $5: 12$. If the area of the triangle is $270 \, cm^2$,then the length of the hypotenuse is .......... $cm$.

The area of the largest circle that can be drawn inside a rectangle with sides $18 \, cm$ and $14 \, cm$ is (in $cm^2$):

One of the diagonals of a rhombus is double the other diagonal. Its area is $25\, cm^{2}$. The sum of the diagonals is.......$cm$

$A$ rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn,which has an area of $240 \, m^2$. If the width of the path is $3 \, m$ and the length of the path is greater than its breadth by $2 \, m$,what is the area of the rectangular plot (in $m^2$)?

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: