In the figure,arcs have been drawn with a rad | vedclass

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(C) Given that the radius of each arc is $r = 21 \, cm$.The area of a sector with central angle $	heta$ is given by $\frac{	heta}{360^{\circ}} 	ime

Vedclass · Accepted Answer

$1386$

Vedclass · Answer

(C) Given that the radius of each arc is $r = 21 \, cm$.The area of a sector with central angle $	heta$ is given by $\frac{	heta}{360^{\circ}} 	imes \pi r^2$.The sum of the areas of the four sectors at vertices $A, B, C,$ and $D$ is:Area $= \frac{\angle A}{360^{\circ}} 	imes \pi r^2 + \frac{\angle B}{360^{\circ}} 	imes \pi r^2 + \frac{\angle C}{360^{\circ}} 	imes \pi r^2 + \frac{\angle D}{360^{\circ}} 	imes \pi r^2$Area $= \frac{(\angle A + \angle B + \angle C + \angle D)}{360^{\circ}} 	imes \pi r^2$Since the sum of the interior angles of any quadrilateral is $360^{\circ}$,we have:Area $= \frac{360^{\circ}}{360^{\circ}} 	imes \pi r^2 = \pi r^2$Substituting $r = 21 \, cm$ and $\pi = \frac{22}{7}$:Area $= \frac{22}{7} 	imes 21 	imes 21 = 22 	imes 3 	imes 21 = 1386 \, cm^2$.Thus,the area of the shaded region is $1386 \, cm^2$.

In the figure,arcs have been drawn with a radius of $21 \, cm$ each,using vertices $A, B, C,$ and $D$ of quadrilateral $ABCD$ as centers. Find the area of the shaded region in $cm^2$.

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