The perimeter of a square is $48\, cm$. The area of a rectangle is $4\, cm^2$ less than the area of the square. If the length of the rectangle is $14\, cm$,then its perimeter is.......$cm$.

In the given figure,there is a large semicircle with diameter $AB = 56 \ cm$. Inside this,there are four smaller identical semicircles with diameters $AE, EF, FG,$ and $GB$ along the diameter $AB$. $A$ circle is inscribed such that it is tangent to the large semicircle and the two middle smaller semicircles. What is the area (in $cm^2$) of the shaded region?

If the length and breadth of a rectangular room are each increased by $1\, m$,then the area of the floor is increased by $21\, m^2$. If the length is increased by $1\, m$ and the breadth is decreased by $1\, m$,then the area is decreased by $5\, m^2$. The perimeter of the floor is.......$m$.

In the given figure,$OP = PQ = 14 \, cm$ and semicircles are drawn on $OP$,$PQ$,and $OQ$ as diameters. Then,the perimeter of the shaded area is . . . . . . $cm$.

The perimeters of five squares are $24 \ cm$,$32 \ cm$,$40 \ cm$,$76 \ cm$,and $80 \ cm$ respectively. The perimeter of another square equal in area to the sum of the areas of these squares is $...... \ cm$.

$ABCD$ is a cyclic quadrilateral. $AB$ and $DC$ when produced meet at $P$. If $PA = 8 \ cm$,$PB = 6 \ cm$,and $PC = 4 \ cm$,then the length (in $cm$) of $PD$ is: