The maximum area of $\Delta ABC$ inscribed in a semicircle with radius $10 \, cm$ is ....... $cm^2$.

As shown in the diagram,$\overline{ OA }$ and $\overline{ OB }$ are two radii of $\odot( O , 21 \text{ cm} )$ perpendicular to each other. If $OD = 10 \text{ cm}$,find the area of the shaded region. (in $\text{cm}^2$)

In a circle with radius $30\,cm$,a minor arc subtends an angle of measure $60^{\circ}$ at the centre. Then,the area of the minor sector formed by that arc is $\ldots \ldots \ldots \ldots$ $cm^{2}$. $(\pi = 3.14)$

The length of minor $\widehat{AB}$ of a circle is $\frac{1}{4}$th of its circumference,then the measure of the angle subtended by minor $\widehat{AB}$ at the centre will be $\ldots .$ (in $^{\circ}$)

The radii of two concentric circles are $14 \, cm$ and $10.5 \, cm$. Then,the difference between their circumferences is $\ldots \ldots \ldots \, cm$.

In the figure,$ABCD$ is a trapezium with $AB \parallel DC$,$AB = 18 \, cm$,$DC = 32 \, cm$,and the distance between $AB$ and $DC = 14 \, cm$. If arcs of equal radii $7 \, cm$ with centers $A, B, C$,and $D$ have been drawn,find the area of the shaded region of the figure (in $cm^2$).