$A$ wire bent in the form of a circle of radius $42 \, cm$ is bent in the form of a rectangle whose sides are in the ratio of $6:5$. The smaller side of the rectangle is (in $cm$)

In the given figure,$ABCD$ is a square of side $14 \ cm$. $E$ and $F$ are mid-points of sides $AB$ and $DC$ respectively. $EPF$ is a semicircle whose diameter is $EF$. $LMNO$ is a square. What is the area (in $cm^2$) of the shaded region?

$A$ bed of roses is shaped as shown in the figure below. In the centre is a square and on each side there is a semi-circle. The side of the square is $21 \, m$. If each rose plant needs $6 \, m^{2}$ of space,then the number of plants in the bed is?

$A$ 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 $ab$?

The perimeter of a triangle is $30 \text{ cm}$ and its area is $30 \text{ cm}^2$. If the largest side measures $13 \text{ cm}$,then what is the length of the smallest side of the triangle? (in $\text{cm}$)

The diagonals of a rhombus are $12 \ cm$ and $16 \ cm$. The length of one side is.......$cm$