The given figure is formed by $2$ quarter circles. The area of the shaded square is $64 {\mathrm{cm}}^2$. Find the perimeter of the figure. (Take $\mathrm{\pi }=\frac{22}{7}$)

 

Calculate the area of shaded region in the given figure, where all of the short line segments are at right angles to each other and $1 \mathrm{cm}$ long.

In the given figure, $△ABC$, is a right-angled triangle, semicircles are drawn on $AB, AC$ and $BC$ as diameters. It is given that $AB=3 \mathrm{cm}$ and $AC=4 \mathrm{cm}$. Find the area of shaded region.

In the given diagram, $PQU$ is an equilateral triangle, $QRVU$ and $RSTU$ are squares. Find the perimeter (in $\mathrm{cm}$) of the whole diagram.

In the given figure (not drawn to scale), $ABCD$ is a rectangle. $ED=16 \mathrm{cm}, FG=FC=8 \mathrm{cm}, BF=20 \mathrm{cm}$ and $FG$ is perpendicular to $BC$. If $CD$ is half of $AD$, then find the area of the shaded region (in ${\mathrm{cm}}^2$).

The area of a square and a rectangle are equal. If the side of the square is $50 \mathrm{cm}$ and the breadth of the rectangle is $30 \mathrm{cm}$. Find:

(i) Length of the rectangle

(ii) Perimeter of the rectangle