The ratio of the area of a sector of a circle to the area of the circle is $1:4$. If the area of the circle is $154 \, cm^2$,the perimeter of the sector is ........ $cm$.

$A$ rectangular paper,when folded into two congruent parts,has a perimeter of $34\, cm$ for each part when folded along one set of sides and a perimeter of $38\, cm$ when folded along the other set of sides. What is the area of the original paper in $cm^2$?

$A$ square has an area of $200\, m^2$. $A$ new square is formed such that the length of its diagonal is $\sqrt{2}$ times the diagonal of the given square. What is the area of the new square in $m^2$?

$A$ rectangle has width $a$ and length $b$. If the width is decreased by $20 \%$ and the length is increased by $10 \%$,what is the area of the new rectangle as a percentage of the original area $ab$?

In the given figure,$ABCD$ is a square. $EFGH$ is a square formed by joining the midpoints of the sides of $ABCD$. $LMNO$ is a square formed by joining the midpoints of the sides of $EFGH$. $A$ circle is inscribed inside $LMNO$. If the area of the circle is $38.5 \text{ cm}^2$,then what is the area (in $\text{cm}^2$) of square $ABCD$?

The breadth of a rectangular plot is $75 \%$ of its length. If the perimeter of the plot is $1050 \, m,$ what is its area (in $, m^2$)?